#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------

#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)

library(tidyverse)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──
## ✓ ggplot2 3.3.3     ✓ purrr   0.3.4
## ✓ tibble  3.0.6     ✓ dplyr   1.0.4
## ✓ tidyr   1.1.2     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
library(lubridate)
## 
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(haven)
library(readxl)
library(mmpack)

#' For ggplots
simple_theme <- theme(
  #aspect.ratio = 1,
  text  = element_text(family="Calibri",size = 12, color = 'black'),
  panel.spacing.y = unit(0,"cm"),
  panel.spacing.x = unit(0.25, "lines"),
  panel.grid.minor = element_line(color = "transparent"),
  panel.grid.major = element_line(color = "transparent"),
  panel.border=element_rect(fill = NA),
  panel.background=element_blank(),
  axis.ticks = element_line(colour = "black"),
  axis.text = element_text(color = "black", size=10),
  # legend.position = c(0.1,0.1),
  plot.margin=grid::unit(c(0,0,0,0), "mm"),
  legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation

set.seed(123)

1 Sensitivty Analysis

In this version of the analysis, we are stratifying by race/ethnicity. This is the script for NHW participants. 05_NPB_Model_BW_v4c.Rmd has the script for all non-NHW participants

1.1 Exposure data

#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
            mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
            cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
            pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
  as.matrix()
head(X)
##       mean_pm  mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 7.454146 48.57052  58.01924      17.205991       31.67281
## [2,] 6.671239 50.06429  61.35590       6.842898       45.00359
## [3,] 6.952053 47.03291  57.13183       9.468662       44.01263
## [4,] 7.071838 46.19062  57.04334       4.563177       65.57617
## [5,] 7.104422 50.67264  59.19456       1.230547       13.83406
## [6,] 7.262078 47.48769  57.41438       8.196283       30.41568
##      mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,]           9048.6468  3350.3033  2992.2968          5211.871
## [2,]           4223.3434  3364.9542  6998.1286          8921.318
## [3,]          10552.9404  3132.8384  3075.6670          5396.864
## [4,]          15609.0030   546.6841   701.0141          3137.313
## [5,]            758.5468  6983.3297  1408.5728          3985.479
## [6,]          10775.8211  2227.6615   617.1256          4116.912
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]          7423.232    36079.21        4887.2996     221.0414     157.6974
## [2,]          9636.816    42235.78        3752.6399     203.8812     142.5368
## [3,]          3903.573    38311.68        5829.9603     204.8360     164.1012
## [4,]          4540.787    42527.04        1408.5747     315.0113     223.5397
## [5,]          3660.698    18821.69         368.4558     233.5437     184.0995
## [6,]          4164.256    36113.37        2984.1470     341.3953     244.7493
##      violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,]           7.636888            46.78194    6.891702  4.564963
## [2,]           2.850212            21.95270    2.725915  5.623583
## [3,]           7.521877            53.88196    8.581395  9.193457
## [4,]          26.089340            99.75336   48.019560 12.475378
## [5,]           8.924274            58.29613    1.166329  3.401797
## [6,]          17.700302            57.79417    8.269720  5.705853
##      pct_limited_eng pct_hh_pov  pct_poc
## [1,]       0.0000000   6.307978 26.63305
## [2,]       1.3506213   9.292274 32.68648
## [3,]       2.9942418  11.516315 36.17576
## [4,]      27.6394850  29.098712 85.33845
## [5,]       0.9844560   0.880829 30.93407
## [6,]       0.8856089  11.512915 57.82769

Variance and histograms of the exposure variables (in their original units):

var(X)
##                               mean_pm          mean_o3      mean_temp
## mean_pm                 0.37533486393   -0.00009847023     0.14642749
## mean_o3                -0.00009847023    8.90678204139    10.81282268
## mean_temp               0.14642749300   10.81282267988    19.23803359
## pct_tree_cover         -0.31562039249   -0.49673758943     0.26736627
## pct_impervious          0.38998516298   -3.36196169567     3.38371752
## mean_aadt_intensity   -40.76212708884  571.26841631737  3039.21948584
## dist_m_tri           -228.65604957972  840.63416900145 -1142.86850331
## dist_m_npl           -327.26389334167  389.22033402881 -1214.35656220
## dist_m_waste_site    -293.39148494029  195.76264386557  -505.75477845
## dist_m_major_emit      75.38286752654  367.90099165114  -601.13695742
## dist_m_cafo         -1799.04879699667 -113.10061840529 -1295.48918289
## dist_m_mine_well     -438.58618797980 -470.07420537707  -698.86208401
## cvd_rate_adj            5.15458179100   -1.76990043482     8.96033736
## res_rate_adj            2.87311588429    0.02209233438    10.86044869
## violent_crime_rate      0.37556375702    0.09420255053     1.16980254
## property_crime_rate     3.74337501727   -6.32086264144     5.99654104
## pct_less_hs             1.11407811657    0.08820859257     1.16622766
## pct_unemp               0.09672587993   -0.14200322662    -0.26389936
## pct_limited_eng         0.46489777874    0.01861635300    -0.06416471
## pct_hh_pov              0.63511223840   -2.17346396822    -0.43383702
## pct_poc                 1.86865059261   -0.72243796509    -1.30303053
##                     pct_tree_cover pct_impervious mean_aadt_intensity
## mean_pm                 -0.3156204      0.3899852           -40.76213
## mean_o3                 -0.4967376     -3.3619617           571.26842
## mean_temp                0.2673663      3.3837175          3039.21949
## pct_tree_cover          14.1689558     12.3764189         12952.91511
## pct_impervious          12.3764189    225.0431814         72329.23445
## mean_aadt_intensity  12952.9151084  72329.2344546      76732213.59795
## dist_m_tri           -1379.0480931 -22311.2104303      -4067115.32674
## dist_m_npl            -667.9200776 -16864.1211853      -3109131.62176
## dist_m_waste_site     2439.0858422  -4500.5284810       1286423.15512
## dist_m_major_emit     -436.0804870  -3795.1383553      -1041488.63725
## dist_m_cafo          13600.2783324  27181.7544247      19866500.22215
## dist_m_mine_well      4340.8882115   5061.5932972       4025007.15834
## cvd_rate_adj           -35.3818150    247.5995298         12773.47708
## res_rate_adj            -5.7237056    206.6624054         41562.89919
## violent_crime_rate      -7.0628378     34.8268766          5586.24923
## property_crime_rate    -41.0349096    215.2833687         32259.22575
## pct_less_hs             -7.7049973     36.5523244          -513.17767
## pct_unemp                0.4702494     16.7021455          6155.35866
## pct_limited_eng         -2.1021233     26.7336819          6276.00173
## pct_hh_pov               3.3644024     71.6622471         23153.87384
## pct_poc                -21.2173929     45.7892837         -6097.13108
##                        dist_m_tri    dist_m_npl dist_m_waste_site
## mean_pm                 -228.6560     -327.2639        -293.39148
## mean_o3                  840.6342      389.2203         195.76264
## mean_temp              -1142.8685    -1214.3566        -505.75478
## pct_tree_cover         -1379.0481     -667.9201        2439.08584
## pct_impervious        -22311.2104   -16864.1212       -4500.52848
## mean_aadt_intensity -4067115.3267 -3109131.6218     1286423.15512
## dist_m_tri           8490021.8257  5223807.4506     2383742.58458
## dist_m_npl           5223807.4506 12187017.8728     4352248.88385
## dist_m_waste_site    2383742.5846  4352248.8838     5182882.45939
## dist_m_major_emit    2128915.6157  7565465.0730     2146855.37143
## dist_m_cafo          1596357.7408  3577908.2118     5528792.90409
## dist_m_mine_well      508901.5232   450437.9950     1628102.57019
## cvd_rate_adj          -54234.0707   -50226.3231      -39856.32468
## res_rate_adj          -37463.4960   -37762.5969      -30012.13465
## violent_crime_rate     -1294.7171    -2173.8745       -4931.44436
## property_crime_rate   -14980.2601   -37647.1447      -34802.06130
## pct_less_hs            -8358.4384    -1944.7470       -5770.15391
## pct_unemp              -1346.7988     2331.6340          55.46268
## pct_limited_eng        -3297.6197     2069.4486        -649.93969
## pct_hh_pov             -7541.4611    -2577.2448       -3859.50474
## pct_poc               -11784.0293     2897.7440       -1796.48889
##                     dist_m_major_emit   dist_m_cafo dist_m_mine_well
## mean_pm                      75.38287    -1799.0488        -438.5862
## mean_o3                     367.90099     -113.1006        -470.0742
## mean_temp                  -601.13696    -1295.4892        -698.8621
## pct_tree_cover             -436.08049    13600.2783        4340.8882
## pct_impervious            -3795.13836    27181.7544        5061.5933
## mean_aadt_intensity    -1041488.63725 19866500.2222     4025007.1583
## dist_m_tri              2128915.61570  1596357.7408      508901.5232
## dist_m_npl              7565465.07295  3577908.2118      450437.9950
## dist_m_waste_site       2146855.37143  5528792.9041     1628102.5702
## dist_m_major_emit      10618148.39450 -5198964.4718    -1562078.1806
## dist_m_cafo            -5198964.47181 59322312.4584    11831250.8310
## dist_m_mine_well       -1562078.18063 11831250.8310     4934706.5090
## cvd_rate_adj              -6735.51280   -63409.9471      -39314.7418
## res_rate_adj             -18729.44986   -31915.1779      -18578.9530
## violent_crime_rate        -3279.14786     -218.4570       -2296.2682
## property_crime_rate      -37357.36924   -39512.2233      -10770.1549
## pct_less_hs                6683.56459   -20906.1580       -8122.5732
## pct_unemp                  3863.27118      360.2569       -1459.2637
## pct_limited_eng            6147.89974    -2449.5928       -3366.9959
## pct_hh_pov                 3537.17769     3206.6101       -2618.1959
## pct_poc                   17131.22545   -37400.8490      -19965.8349
##                      cvd_rate_adj    res_rate_adj violent_crime_rate
## mean_pm                  5.154582      2.87311588         0.37556376
## mean_o3                 -1.769900      0.02209233         0.09420255
## mean_temp                8.960337     10.86044869         1.16980254
## pct_tree_cover         -35.381815     -5.72370563        -7.06283776
## pct_impervious         247.599530    206.66240537        34.82687661
## mean_aadt_intensity  12773.477081  41562.89918523      5586.24922880
## dist_m_tri          -54234.070749 -37463.49600671     -1294.71708456
## dist_m_npl          -50226.323102 -37762.59685160     -2173.87453741
## dist_m_waste_site   -39856.324678 -30012.13464859     -4931.44436485
## dist_m_major_emit    -6735.512802 -18729.44985583     -3279.14786226
## dist_m_cafo         -63409.947058 -31915.17788201      -218.45697058
## dist_m_mine_well    -39314.741764 -18578.95304228     -2296.26822650
## cvd_rate_adj          2191.182815   1385.29494365       150.70808516
## res_rate_adj          1385.294944   1156.71343313       121.65371220
## violent_crime_rate     150.708085    121.65371220        53.66783212
## property_crime_rate    566.337526    472.63650773       256.55496614
## pct_less_hs            231.479433    145.54238485        16.54740871
## pct_unemp               67.363344     51.69113046         9.04149094
## pct_limited_eng        110.257122     67.33790262         9.28416690
## pct_hh_pov             181.657547    152.91320652        25.02326808
## pct_poc                494.097173    253.35297277        39.91113843
##                     property_crime_rate     pct_less_hs      pct_unemp
## mean_pm                        3.743375      1.11407812     0.09672588
## mean_o3                       -6.320863      0.08820859    -0.14200323
## mean_temp                      5.996541      1.16622766    -0.26389936
## pct_tree_cover               -41.034910     -7.70499732     0.47024939
## pct_impervious               215.283369     36.55232441    16.70214553
## mean_aadt_intensity        32259.225754   -513.17766924  6155.35865920
## dist_m_tri                -14980.260099  -8358.43835664 -1346.79876430
## dist_m_npl                -37647.144722  -1944.74702528  2331.63404217
## dist_m_waste_site         -34802.061301  -5770.15391068    55.46268468
## dist_m_major_emit         -37357.369240   6683.56458897  3863.27117705
## dist_m_cafo               -39512.223334 -20906.15798373   360.25692941
## dist_m_mine_well          -10770.154916  -8122.57321486 -1459.26372738
## cvd_rate_adj                 566.337526    231.47943304    67.36334415
## res_rate_adj                 472.636508    145.54238485    51.69113046
## violent_crime_rate           256.554966     16.54740871     9.04149094
## property_crime_rate         2092.599784      2.37207933    -4.44996391
## pct_less_hs                    2.372079    100.97051611    24.75412746
## pct_unemp                     -4.449964     24.75412746    16.99668272
## pct_limited_eng              -10.993591     45.55561336    14.53021864
## pct_hh_pov                    85.141940     53.74957643    22.28487081
## pct_poc                      -32.166948    167.47523501    53.90073829
##                     pct_limited_eng    pct_hh_pov       pct_poc
## mean_pm                  0.46489778     0.6351122      1.868651
## mean_o3                  0.01861635    -2.1734640     -0.722438
## mean_temp               -0.06416471    -0.4338370     -1.303031
## pct_tree_cover          -2.10212332     3.3644024    -21.217393
## pct_impervious          26.73368187    71.6622471     45.789284
## mean_aadt_intensity   6276.00173099 23153.8738357  -6097.131081
## dist_m_tri           -3297.61965954 -7541.4610842 -11784.029327
## dist_m_npl            2069.44857387 -2577.2447547   2897.744008
## dist_m_waste_site     -649.93968840 -3859.5047430  -1796.488891
## dist_m_major_emit     6147.89973970  3537.1776917  17131.225451
## dist_m_cafo          -2449.59276096  3206.6101083 -37400.848996
## dist_m_mine_well     -3366.99587133 -2618.1959480 -19965.834924
## cvd_rate_adj           110.25712151   181.6575467    494.097173
## res_rate_adj            67.33790262   152.9132065    253.352973
## violent_crime_rate       9.28416690    25.0232681     39.911138
## property_crime_rate    -10.99359078    85.1419396    -32.166948
## pct_less_hs             45.55561336    53.7495764    167.475235
## pct_unemp               14.53021864    22.2848708     53.900738
## pct_limited_eng         35.59148773    34.6946706     90.364663
## pct_hh_pov              34.69467062    75.9843174     96.120981
## pct_poc                 90.36466320    96.1209811    431.057094
ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Scaling the exposure variables

X.scaled <- apply(X, 2, scale)
head(X.scaled)
##          mean_pm    mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] -0.04466117  0.2557710  1.258916      2.8650572     -0.4317392
## [2,] -1.32257091  0.7562940  2.019647      0.1119669      0.4568939
## [3,] -0.86420910 -0.2594409  1.056593      0.8095353      0.3908364
## [4,] -0.66868869 -0.5416715  1.036418     -0.4936707      1.8282681
## [5,] -0.61550307  0.9601351  1.526878     -1.3790272     -1.6208750
## [6,] -0.35816558 -0.1070584  1.121012      0.4715111     -0.5155396
##      mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,]         -0.09084216 -0.2344047 -0.6085424        0.03971116
## [2,]         -0.64169521 -0.2293766  0.5389346        1.66909525
## [3,]          0.08088689 -0.3090384 -0.5846609        0.12096980
## [4,]          0.65808323 -1.1966032 -1.2648840       -0.87154355
## [5,]         -1.03723382  1.0124451 -1.0622027       -0.49898458
## [6,]          0.10633078 -0.6196939 -1.2889140       -0.44125230
##      dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,]       -0.02150275  -0.1312893     0.5115705609  -0.21472100  -0.02194817
## [2,]        0.65781307   0.6680473     0.0007893036  -0.58131344  -0.46770979
## [3,]       -1.10163310   0.1585630     0.9359211172  -0.56091550   0.16634114
## [4,]       -0.90608162   0.7058640    -1.0544209929   1.79274970   1.91399256
## [5,]       -1.17616773  -2.3719154    -1.5226435621   0.05236468   0.75434311
## [6,]       -1.02163351  -0.1268541    -0.3451574045   2.35639005   2.53761051
##      violent_crime_rate property_crime_rate pct_less_hs  pct_unemp
## [1,]         -0.5964233        -0.258738271  -0.4702609 -0.8122686
## [2,]         -1.2498200        -0.801513939  -0.8848327 -0.5554906
## [3,]         -0.6121227        -0.103529459  -0.3021056  0.3104157
## [4,]          1.9223962         0.899234905   3.6227114  1.1064759
## [5,]         -0.4206909        -0.007034139  -1.0400400 -1.0944053
## [6,]          0.7772654        -0.018007256  -0.3331230 -0.5355351
##      pct_limited_eng  pct_hh_pov    pct_poc
## [1,]      -0.8611272 -0.63784322 -0.8362933
## [2,]      -0.6347355 -0.29548558 -0.5447291
## [3,]      -0.3592312 -0.04034434 -0.3766674
## [4,]       3.7718149  1.97670312  1.9912592
## [5,]      -0.6961123 -1.26044411 -0.6291337
## [6,]      -0.7126811 -0.04073434  0.6662003

Variance and histograms of the exposure variables (scaled):

var(X.scaled)
##                            mean_pm        mean_o3    mean_temp pct_tree_cover
## mean_pm              1.00000000000 -0.00005385612  0.054492011    -0.13686320
## mean_o3             -0.00005385612  1.00000000000  0.826034772    -0.04421786
## mean_temp            0.05449201081  0.82603477185  1.000000000     0.01619412
## pct_tree_cover      -0.13686319671 -0.04421785696  0.016194120     1.00000000
## pct_impervious       0.04243319193 -0.07509299382  0.051425773     0.21917608
## mean_aadt_intensity -0.00759553767  0.02185198723  0.079102983     0.39283460
## dist_m_tri          -0.12809106580  0.09667011226 -0.089425530    -0.12573497
## dist_m_npl          -0.15301708182  0.03735823800 -0.079308030    -0.05082845
## dist_m_waste_site   -0.21035477359  0.02881268488 -0.050649362     0.28462463
## dist_m_major_emit    0.03776059293  0.03783085448 -0.042059944    -0.03555276
## dist_m_cafo         -0.38126281823 -0.00492034473 -0.038348150     0.46910476
## dist_m_mine_well    -0.32226625571 -0.07090475229 -0.071726638     0.51913345
## cvd_rate_adj         0.17973997428 -0.01266919781  0.043642007    -0.20080378
## res_rate_adj         0.13788937407  0.00021765483  0.072803882    -0.04470905
## violent_crime_rate   0.08367913752  0.00430868974  0.036406187    -0.25612577
## property_crime_rate  0.13357057516 -0.04629913234  0.029886660    -0.23830956
## pct_less_hs          0.18097096497  0.00294139393  0.026460967    -0.20370715
## pct_unemp            0.03829580051 -0.01154132622 -0.014594053     0.03030241
## pct_limited_eng      0.12719643719  0.00104558928 -0.002452126    -0.09360870
## pct_hh_pov           0.11892661145 -0.08354684403 -0.011347084     0.10253616
## pct_poc              0.14690996353 -0.01165930732 -0.014308920    -0.27149116
##                     pct_impervious mean_aadt_intensity  dist_m_tri  dist_m_npl
## mean_pm                 0.04243319        -0.007595538 -0.12809107 -0.15301708
## mean_o3                -0.07509299         0.021851987  0.09667011  0.03735824
## mean_temp               0.05142577         0.079102983 -0.08942553 -0.07930803
## pct_tree_cover          0.21917608         0.392834601 -0.12573497 -0.05082845
## pct_impervious          1.00000000         0.550417300 -0.51042954 -0.32201942
## mean_aadt_intensity     0.55041730         1.000000000 -0.15934675 -0.10167204
## dist_m_tri             -0.51042954        -0.159346754  1.00000000  0.51355154
## dist_m_npl             -0.32201942        -0.101672036  0.51355154  1.00000000
## dist_m_waste_site      -0.13177860         0.064507365  0.35935134  0.54762002
## dist_m_major_emit      -0.07763728        -0.036487262  0.22422274  0.66506258
## dist_m_cafo             0.23525319         0.294458074  0.07113229  0.13306733
## dist_m_mine_well        0.15188807         0.206846001  0.07862283  0.05808388
## cvd_rate_adj            0.35259616         0.031151643 -0.39762941 -0.30735717
## res_rate_adj            0.40505655         0.139509596 -0.37804283 -0.31805354
## violent_crime_rate      0.31690170         0.087051131 -0.06065456 -0.08500192
## property_crime_rate     0.31371441         0.080504839 -0.11238850 -0.23574377
## pct_less_hs             0.24248495        -0.005830175 -0.28547853 -0.05543922
## pct_unemp               0.27005813         0.170444274 -0.11211565  0.16200543
## pct_limited_eng         0.29871207         0.120093947 -0.18970252  0.09936486
## pct_hh_pov              0.54801887         0.303230454 -0.29691976 -0.08469250
## pct_poc                 0.14701563        -0.033525037 -0.19479240  0.03998010
##                     dist_m_waste_site dist_m_major_emit  dist_m_cafo
## mean_pm                   -0.21035477        0.03776059 -0.381262818
## mean_o3                    0.02881268        0.03783085 -0.004920345
## mean_temp                 -0.05064936       -0.04205994 -0.038348150
## pct_tree_cover             0.28462463       -0.03555276  0.469104758
## pct_impervious            -0.13177860       -0.07763728  0.235253189
## mean_aadt_intensity        0.06450737       -0.03648726  0.294458074
## dist_m_tri                 0.35935134        0.22422274  0.071132289
## dist_m_npl                 0.54762002        0.66506258  0.133067328
## dist_m_waste_site          1.00000000        0.28939613  0.315308448
## dist_m_major_emit          0.28939613        1.00000000 -0.207149275
## dist_m_cafo                0.31530845       -0.20714928  1.000000000
## dist_m_mine_well           0.32193294       -0.21579814  0.691498053
## cvd_rate_adj              -0.37400057       -0.04415775 -0.175877000
## res_rate_adj              -0.38761298       -0.16900040 -0.121835919
## violent_crime_rate        -0.29568646       -0.13736610 -0.003871683
## property_crime_rate       -0.33417673       -0.25061600 -0.112144852
## pct_less_hs               -0.25223447        0.20412043 -0.270126943
## pct_unemp                  0.00590926        0.28757340  0.011345437
## pct_limited_eng           -0.04785357        0.31624911 -0.053310381
## pct_hh_pov                -0.19448402        0.12452900  0.047761190
## pct_poc                   -0.03800769        0.25321920 -0.233886431
##                     dist_m_mine_well cvd_rate_adj  res_rate_adj
## mean_pm                  -0.32226626   0.17973997  0.1378893741
## mean_o3                  -0.07090475  -0.01266920  0.0002176548
## mean_temp                -0.07172664   0.04364201  0.0728038823
## pct_tree_cover            0.51913345  -0.20080378 -0.0447090537
## pct_impervious            0.15188807   0.35259616  0.4050565514
## mean_aadt_intensity       0.20684600   0.03115164  0.1395095959
## dist_m_tri                0.07862283  -0.39762941 -0.3780428333
## dist_m_npl                0.05808388  -0.30735717 -0.3180535435
## dist_m_waste_site         0.32193294  -0.37400057 -0.3876129844
## dist_m_major_emit        -0.21579814  -0.04415775 -0.1690004014
## dist_m_cafo               0.69149805  -0.17587700 -0.1218359191
## dist_m_mine_well          1.00000000  -0.37808153 -0.2459108457
## cvd_rate_adj             -0.37808153   1.00000000  0.8701418420
## res_rate_adj             -0.24591085   0.87014184  1.0000000000
## violent_crime_rate       -0.14110257   0.43948112  0.4882648378
## property_crime_rate      -0.10598593   0.26448007  0.3037884703
## pct_less_hs              -0.36388628   0.49212544  0.4258722177
## pct_unemp                -0.15933862   0.34906174  0.3686557880
## pct_limited_eng          -0.25406149   0.39481557  0.3318743018
## pct_hh_pov               -0.13521021   0.44519692  0.5157866800
## pct_poc                  -0.43290182   0.50840014  0.3587944499
##                     violent_crime_rate property_crime_rate  pct_less_hs
## mean_pm                    0.083679138         0.133570575  0.180970965
## mean_o3                    0.004308690        -0.046299132  0.002941394
## mean_temp                  0.036406187         0.029886660  0.026460967
## pct_tree_cover            -0.256125773        -0.238309563 -0.203707154
## pct_impervious             0.316901702         0.313714407  0.242484946
## mean_aadt_intensity        0.087051131         0.080504839 -0.005830175
## dist_m_tri                -0.060654559        -0.112388497 -0.285478530
## dist_m_npl                -0.085001918        -0.235743774 -0.055439219
## dist_m_waste_site         -0.295686456        -0.334176726 -0.252234466
## dist_m_major_emit         -0.137366103        -0.250616004  0.204120426
## dist_m_cafo               -0.003871683        -0.112144852 -0.270126943
## dist_m_mine_well          -0.141102571        -0.105985926 -0.363886281
## cvd_rate_adj               0.439481116         0.264480066  0.492125439
## res_rate_adj               0.488264838         0.303788470  0.425872218
## violent_crime_rate         1.000000000         0.765561899  0.224789323
## property_crime_rate        0.765561899         1.000000000  0.005160465
## pct_less_hs                0.224789323         0.005160465  1.000000000
## pct_unemp                  0.299364943        -0.023595616  0.597541745
## pct_limited_eng            0.212428529        -0.040283149  0.759926412
## pct_hh_pov                 0.391854663         0.213519954  0.613642986
## pct_poc                    0.262403541        -0.033868765  0.802760342
##                       pct_unemp pct_limited_eng  pct_hh_pov     pct_poc
## mean_pm              0.03829580     0.127196437  0.11892661  0.14690996
## mean_o3             -0.01154133     0.001045589 -0.08354684 -0.01165931
## mean_temp           -0.01459405    -0.002452126 -0.01134708 -0.01430892
## pct_tree_cover       0.03030241    -0.093608696  0.10253616 -0.27149116
## pct_impervious       0.27005813     0.298712073  0.54801887  0.14701563
## mean_aadt_intensity  0.17044427     0.120093947  0.30323045 -0.03352504
## dist_m_tri          -0.11211565    -0.189702515 -0.29691976 -0.19479240
## dist_m_npl           0.16200543     0.099364864 -0.08469250  0.03998010
## dist_m_waste_site    0.00590926    -0.047853566 -0.19448402 -0.03800769
## dist_m_major_emit    0.28757340     0.316249109  0.12452900  0.25321920
## dist_m_cafo          0.01134544    -0.053310381  0.04776119 -0.23388643
## dist_m_mine_well    -0.15933862    -0.254061495 -0.13521021 -0.43290182
## cvd_rate_adj         0.34906174     0.394815571  0.44519692  0.50840014
## res_rate_adj         0.36865579     0.331874302  0.51578668  0.35879445
## violent_crime_rate   0.29936494     0.212428529  0.39185466  0.26240354
## property_crime_rate -0.02359562    -0.040283149  0.21351995 -0.03386877
## pct_less_hs          0.59754175     0.759926412  0.61364299  0.80276034
## pct_unemp            1.00000000     0.590768043  0.62010617  0.62971673
## pct_limited_eng      0.59076804     1.000000000  0.66715649  0.72955521
## pct_hh_pov           0.62010617     0.667156489  1.00000000  0.53111530
## pct_poc              0.62971673     0.729555212  0.53111530  1.00000000
ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.2 Covariate data

Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.

W <- select(hs_data2, 
            lat, lon, lat_lon_int,
            ed_no_hs, ed_hs, ed_aa, ed_4yr,
            low_bmi, ovwt_bmi, obese_bmi,
            concep_spring, concep_summer, concep_fall,
            concep_2010, concep_2011, concep_2012, concep_2013,
            maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
            male, gest_age_w) %>%
  as.matrix()
head(W)
##           lat       lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,] 39.74934 -104.9129   -4170.219        0     0     0      0       0
## [2,] 39.68397 -104.8933   -4162.583        0     0     1      0       0
## [3,] 39.77109 -105.0477   -4177.861        0     0     0      1       0
## [4,] 39.71579 -105.0205   -4170.971        0     1     0      0       0
## [5,] 39.88283 -104.7784   -4178.860        0     0     1      0       0
## [6,] 39.75980 -104.9562   -4173.037        0     0     0      0       0
##      ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,]        0         0             0             0           0           1
## [2,]        0         0             1             0           0           1
## [3,]        0         0             0             0           0           1
## [4,]        0         1             1             0           0           1
## [5,]        0         0             1             0           0           1
## [6,]        0         0             0             0           0           1
##      concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,]           0           0           0           34          0       0
## [2,]           0           0           0           28          0       0
## [3,]           0           0           0           33          0       0
## [4,]           0           0           0           31          0       0
## [5,]           0           0           0           31          0       0
## [6,]           0           0           0           36          1       0
##      mean_cpss mean_epsd male gest_age_w
## [1,]        19         1    0   40.42857
## [2,]        20         0    0   36.28571
## [3,]        22         4    1   41.57143
## [4,]        17         0    1   41.00000
## [5,]        23         9    0   38.57143
## [6,]        21         5    0   40.57143

Scaled the non-binary (continuous) covariates

colnames(W)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"          "gest_age_w"
W.s <- apply(W[,c(1, 2, 3, 18, 21, 22, 24)], 2, scale) #' just the continuous ones

W.scaled <- cbind(W.s[,1:3],
                  W[,4:17], W.s[,4],
                  W[,19:20], W.s[,5:6],
                  W[,23], W.s[,7])
colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   ""              "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     ""              ""
colnames(W.scaled) <- colnames(W)
head(W.scaled)
##             lat        lon lat_lon_int ed_no_hs ed_hs ed_aa ed_4yr low_bmi
## [1,]  0.2674191 -0.4798892  -0.4051852        0     0     0      0       0
## [2,] -0.5948425 -0.2716453   0.3840107        0     0     1      0       0
## [3,]  0.5542857 -1.9109032  -1.1949511        0     0     0      1       0
## [4,] -0.1750665 -1.6218003  -0.4829104        0     1     0      0       0
## [5,]  2.0281845  0.9480022  -1.2981784        0     0     1      0       0
## [6,]  0.4054444 -0.9392257  -0.6964047        0     0     0      0       0
##      ovwt_bmi obese_bmi concep_spring concep_summer concep_fall concep_2010
## [1,]        0         0             0             0           0           1
## [2,]        0         0             1             0           0           1
## [3,]        0         0             0             0           0           1
## [4,]        0         1             1             0           0           1
## [5,]        0         0             1             0           0           1
## [6,]        0         0             0             0           0           1
##      concep_2011 concep_2012 concep_2013 maternal_age any_smoker smokeSH
## [1,]           0           0           0    0.7414877          0       0
## [2,]           0           0           0   -0.4540269          0       0
## [3,]           0           0           0    0.5422353          0       0
## [4,]           0           0           0    0.1437304          0       0
## [5,]           0           0           0    0.1437304          0       0
## [6,]           0           0           0    1.1399926          1       0
##        mean_cpss   mean_epsd male gest_age_w
## [1,]  0.03508979 -0.95840046    0  0.5959769
## [2,]  0.42874413 -1.31067596    0 -2.2254033
## [3,]  1.21605281  0.09842604    1  1.3742887
## [4,] -0.75221889 -1.31067596    1  0.9851328
## [5,]  1.60970715  1.85980354    0 -0.6687797
## [6,]  0.82239847  0.45070154    0  0.6932659
summary(W.scaled)
##       lat                lon           lat_lon_int            ed_no_hs      
##  Min.   :-2.14565   Min.   :-2.1021   Min.   :-3.0142020   Min.   :0.00000  
##  1st Qu.:-0.61475   1st Qu.:-0.6902   1st Qu.:-0.4724605   1st Qu.:0.00000  
##  Median : 0.06549   Median :-0.0679   Median : 0.0003061   Median :0.00000  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   : 0.0000000   Mean   :0.05393  
##  3rd Qu.: 0.38409   3rd Qu.: 0.7585   3rd Qu.: 0.6626216   3rd Qu.:0.00000  
##  Max.   : 3.33626   Max.   : 4.1076   Max.   : 2.3009871   Max.   :1.00000  
##      ed_hs             ed_aa            ed_4yr          low_bmi       
##  Min.   :0.00000   Min.   :0.0000   Min.   :0.0000   Min.   :0.00000  
##  1st Qu.:0.00000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.00000  
##  Median :0.00000   Median :0.0000   Median :0.0000   Median :0.00000  
##  Mean   :0.08315   Mean   :0.1618   Mean   :0.3303   Mean   :0.03146  
##  3rd Qu.:0.00000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:0.00000  
##  Max.   :1.00000   Max.   :1.0000   Max.   :1.0000   Max.   :1.00000  
##     ovwt_bmi        obese_bmi      concep_spring    concep_summer   
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.2315   Mean   :0.1393   Mean   :0.2494   Mean   :0.2629  
##  3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:0.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_fall      concep_2010      concep_2011      concep_2012    
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.0000   Median :0.0000   Median :0.0000  
##  Mean   :0.2584   Mean   :0.1573   Mean   :0.2876   Mean   :0.2966  
##  3rd Qu.:1.0000   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :1.0000   Max.   :1.0000   Max.   :1.0000  
##   concep_2013      maternal_age       any_smoker         smokeSH     
##  Min.   :0.0000   Min.   :-2.8451   Min.   :0.00000   Min.   :0.000  
##  1st Qu.:0.0000   1st Qu.:-0.6533   1st Qu.:0.00000   1st Qu.:0.000  
##  Median :0.0000   Median : 0.1437   Median :0.00000   Median :0.000  
##  Mean   :0.2584   Mean   : 0.0000   Mean   :0.06966   Mean   :0.182  
##  3rd Qu.:1.0000   3rd Qu.: 0.7415   3rd Qu.:0.00000   3rd Qu.:0.000  
##  Max.   :1.0000   Max.   : 2.7340   Max.   :1.00000   Max.   :1.000  
##    mean_cpss          mean_epsd            male          gest_age_w     
##  Min.   :-4.68876   Min.   :-1.3107   Min.   :0.0000   Min.   :-6.8953  
##  1st Qu.:-0.62100   1st Qu.:-0.7823   1st Qu.:0.0000   1st Qu.:-0.4742  
##  Median : 0.03509   Median :-0.1364   Median :1.0000   Median : 0.1095  
##  Mean   : 0.00000   Mean   : 0.0000   Mean   :0.5124   Mean   : 0.0000  
##  3rd Qu.: 0.69118   3rd Qu.: 0.4507   3rd Qu.:1.0000   3rd Qu.: 0.5960  
##  Max.   : 2.98750   Max.   : 3.9735   Max.   :1.0000   Max.   : 1.8607

Variance and histograms for the scaled covariates

var(W.scaled)
##                        lat          lon  lat_lon_int      ed_no_hs
## lat            1.000000000 -0.276115615 -0.928356863 -0.0101130332
## lon           -0.276115615  1.000000000  0.613573495  0.0262079705
## lat_lon_int   -0.928356863  0.613573495  1.000000000  0.0184474549
## ed_no_hs      -0.010113033  0.026207970  0.018447455  0.0511387792
## ed_hs         -0.016953107  0.027192891  0.024434547 -0.0044943820
## ed_aa         -0.020229967  0.076553174  0.046240217 -0.0087458245
## ed_4yr         0.015291929 -0.006510708 -0.015091570 -0.0178560583
## low_bmi       -0.005196646  0.003764983  0.005725894 -0.0017005770
## ovwt_bmi       0.016939252 -0.007162408 -0.016707589 -0.0080068833
## obese_bmi      0.019720120  0.026026302 -0.006128656  0.0059823869
## concep_spring  0.042294895 -0.001716481 -0.035419198  0.0067871242
## concep_summer -0.039711819  0.018991239  0.039990266 -0.0074552080
## concep_fall    0.005023840 -0.001305642 -0.004645539 -0.0004555117
## concep_2010    0.002951929 -0.003179720 -0.003684401  0.0050106286
## concep_2011   -0.044325781  0.037270498  0.050823044 -0.0020346189
## concep_2012   -0.007398114 -0.012020792  0.001446144  0.0019840065
## concep_2013    0.048771966 -0.022069986 -0.048584788 -0.0049600162
## maternal_age   0.109210499 -0.272870082 -0.195251338 -0.0909594732
## any_smoker    -0.010940646  0.030990243  0.020970244  0.0232614637
## smokeSH       -0.043143276  0.060472659  0.058815490  0.0352059925
## mean_cpss     -0.027134738 -0.052301539  0.002117103 -0.0204162448
## mean_epsd     -0.046036525 -0.011368895  0.033428064  0.0523961815
## male           0.027341149 -0.032250065 -0.034932167 -0.0029203361
## gest_age_w    -0.016388845 -0.005364562  0.011370938 -0.0017485228
##                       ed_hs         ed_aa         ed_4yr       low_bmi
## lat           -0.0169531065 -0.0202299672  0.01529192857 -0.0051966462
## lon            0.0271928911  0.0765531735 -0.00651070784  0.0037649829
## lat_lon_int    0.0244345472  0.0462402175 -0.01509157026  0.0057258937
## ed_no_hs      -0.0044943820 -0.0087458245 -0.01785605831 -0.0017005770
## ed_hs          0.0764044944 -0.0134831461 -0.02752808989  0.0018827817
## ed_aa         -0.0134831461  0.1359246887 -0.05356817492  0.0016550258
## ed_4yr        -0.0275280899 -0.0535681749  0.22171272396 -0.0014070250
## low_bmi        0.0018827817  0.0016550258 -0.00140702500  0.0305395283
## ovwt_bmi      -0.0057748760  0.0210243952  0.01120558761 -0.0072983095
## obese_bmi      0.0199210446  0.0089381516 -0.01234436684 -0.0043931572
## concep_spring -0.0005162466  0.0023433546 -0.00150318858 -0.0078651685
## concep_summer -0.0016398421 -0.0088521105  0.00529405810  0.0007186962
## concep_fall    0.0054914465  0.0008857172  0.00002530621  0.0098694200
## concep_2010    0.0116661605  0.0082751291 -0.00703512501  0.0017967406
## concep_2011   -0.0014475149  0.0006529001  0.01963255390  0.0021915174
## concep_2012   -0.0044488309 -0.0075614941 -0.00811823059 -0.0071009211
## concep_2013   -0.0057698148 -0.0013665351 -0.00447919830  0.0031126632
## maternal_age  -0.0759807484 -0.0511876462  0.02873821574 -0.0035457615
## any_smoker     0.0099605223  0.0022168236 -0.01630731855 -0.0021965786
## smokeSH        0.0253720012  0.0177801397 -0.02873266525 -0.0012349428
## mean_cpss     -0.0384509319  0.0222402682  0.01516400036 -0.0008145512
## mean_epsd      0.0080699343  0.0319614805 -0.02810911729  0.0027068171
## male          -0.0021560887 -0.0155177650  0.00604312177 -0.0003897156
## gest_age_w    -0.0173857629 -0.0026161368  0.00449169959  0.0047684300
##                   ovwt_bmi     obese_bmi concep_spring concep_summer
## lat            0.016939252  0.0197201196  0.0422948947 -0.0397118186
## lon           -0.007162408  0.0260263016 -0.0017164811  0.0189912393
## lat_lon_int   -0.016707589 -0.0061286565 -0.0354191979  0.0399902664
## ed_no_hs      -0.008006883  0.0059823869  0.0067871242 -0.0074552080
## ed_hs         -0.005774876  0.0199210446 -0.0005162466 -0.0016398421
## ed_aa          0.021024395  0.0089381516  0.0023433546 -0.0088521105
## ed_4yr         0.011205588 -0.0123443668 -0.0015031886  0.0052940581
## low_bmi       -0.007298310 -0.0043931572 -0.0078651685  0.0007186962
## ovwt_bmi       0.178287276 -0.0323210851  0.0142069035  0.0043222998
## obese_bmi     -0.032321085  0.1201842292  0.0012045754  0.0015740460
## concep_spring  0.014206904  0.0012045754  0.1876404494 -0.0657303371
## concep_summer  0.004322300  0.0015740460 -0.0657303371  0.1942301852
## concep_fall   -0.001391841 -0.0090596214 -0.0646067416 -0.0680989979
## concep_2010    0.001796741 -0.0084522725 -0.0235600769 -0.0099200324
## concep_2011   -0.003664338  0.0161402976 -0.0065947970  0.0075361879
## concep_2012   -0.005749570 -0.0008806559 -0.0065897358  0.0164287883
## concep_2013    0.007617168 -0.0068073692  0.0367446098 -0.0140449438
## maternal_age   0.037381766 -0.0019191081 -0.0107391395  0.0118464337
## any_smoker    -0.007151534  0.0082903128  0.0006022877 -0.0025913554
## smokeSH       -0.006189898  0.0173752404 -0.0117218342 -0.0006680838
## mean_cpss      0.015971910 -0.0036706272 -0.0079253536  0.0051091252
## mean_epsd      0.010535162  0.0280256157 -0.0226015810 -0.0051387625
## male          -0.003993319 -0.0062303877  0.0070452475  0.0046259743
## gest_age_w    -0.060704419 -0.0125331320 -0.0199467506  0.0117718770
##                  concep_fall  concep_2010   concep_2011   concep_2012
## lat            0.00502384034  0.002951929 -0.0443257810 -0.0073981137
## lon           -0.00130564175 -0.003179720  0.0372704984 -0.0120207920
## lat_lon_int   -0.00464553856 -0.003684401  0.0508230437  0.0014461445
## ed_no_hs      -0.00045551169  0.005010629 -0.0020346189  0.0019840065
## ed_hs          0.00549144650  0.011666161 -0.0014475149 -0.0044488309
## ed_aa          0.00088571718  0.008275129  0.0006529001 -0.0075614941
## ed_4yr         0.00002530621 -0.007035125  0.0196325539 -0.0081182306
## low_bmi        0.00986941998  0.001796741  0.0021915174 -0.0071009211
## ovwt_bmi      -0.00139184128  0.001796741 -0.0036643385 -0.0057495698
## obese_bmi     -0.00905962142 -0.008452272  0.0161402976 -0.0008806559
## concep_spring -0.06460674157 -0.023560077 -0.0065947970 -0.0065897358
## concep_summer -0.06809899787 -0.009920032  0.0075361879  0.0164287883
## concep_fall    0.19207409657  0.035833586 -0.0136906569 -0.0070098188
## concep_2010    0.03583358640  0.132857577 -0.0453487195 -0.0467658670
## concep_2011   -0.01369065695 -0.045348720  0.2053649155 -0.0855147282
## concep_2012   -0.00700981881 -0.046765867 -0.0855147282  0.2091102338
## concep_2013   -0.01513311064 -0.040742990 -0.0745014678 -0.0768296386
## maternal_age  -0.02021467293 -0.045103579 -0.0182501839  0.0175997242
## any_smoker    -0.00452981071  0.007035125  0.0001872659 -0.0094493370
## smokeSH       -0.00210041502  0.009591052  0.0060836117 -0.0135742484
## mean_cpss     -0.02460256616  0.008339769  0.0065695393 -0.0157228628
## mean_epsd     -0.00756565630 -0.003656536  0.0347223805 -0.0348724455
## male          -0.00883186557 -0.008705335 -0.0080676182 -0.0126834700
## gest_age_w     0.02968451108  0.010914111  0.0166767027 -0.0384310645
##                concep_2013 maternal_age    any_smoker       smokeSH
## lat            0.048771966  0.109210499 -0.0109406462 -0.0431432763
## lon           -0.022069986 -0.272870082  0.0309902425  0.0604726586
## lat_lon_int   -0.048584788 -0.195251338  0.0209702437  0.0588154897
## ed_no_hs      -0.004960016 -0.090959473  0.0232614637  0.0352059925
## ed_hs         -0.005769815 -0.075980748  0.0099605223  0.0253720012
## ed_aa         -0.001366535 -0.051187646  0.0022168236  0.0177801397
## ed_4yr        -0.004479198  0.028738216 -0.0163073186 -0.0287326652
## low_bmi        0.003112663 -0.003545762 -0.0021965786 -0.0012349428
## ovwt_bmi       0.007617168  0.037381766 -0.0071515336 -0.0061898978
## obese_bmi     -0.006807369 -0.001919108  0.0082903128  0.0173752404
## concep_spring  0.036744610 -0.010739140  0.0006022877 -0.0117218342
## concep_summer -0.014044944  0.011846434 -0.0025913554 -0.0006680838
## concep_fall   -0.015133111 -0.020214673 -0.0045298107 -0.0021004150
## concep_2010   -0.040742990 -0.045103579  0.0070351250  0.0095910517
## concep_2011   -0.074501468 -0.018250184  0.0001872659  0.0060836117
## concep_2012   -0.076829639  0.017599724 -0.0094493370 -0.0135742484
## concep_2013    0.192074097  0.045754039  0.0022269460 -0.0021004150
## maternal_age   0.045754039  1.000000000 -0.0649088156 -0.1555294446
## any_smoker     0.002226946 -0.064908816  0.0649559672  0.0458497824
## smokeSH       -0.002100415 -0.155529445  0.0458497824  0.1492256301
## mean_cpss      0.000813555  0.109685178  0.0088039929 -0.0046810956
## mean_epsd      0.003806601 -0.112036096  0.0487907570  0.1019256746
## male           0.029456423 -0.014599542  0.0115244458  0.0056281000
## gest_age_w     0.010840251  0.017621395 -0.0096629152 -0.0275666860
##                   mean_cpss    mean_epsd          male   gest_age_w
## lat           -0.0271347383 -0.046036525  0.0273411490 -0.016388845
## lon           -0.0523015387 -0.011368895 -0.0322500653 -0.005364562
## lat_lon_int    0.0021171030  0.033428064 -0.0349321671  0.011370938
## ed_no_hs      -0.0204162448  0.052396181 -0.0029203361 -0.001748523
## ed_hs         -0.0384509319  0.008069934 -0.0021560887 -0.017385763
## ed_aa          0.0222402682  0.031961481 -0.0155177650 -0.002616137
## ed_4yr         0.0151640004 -0.028109117  0.0060431218  0.004491700
## low_bmi       -0.0008145512  0.002706817 -0.0003897156  0.004768430
## ovwt_bmi       0.0159719102  0.010535162 -0.0039933192 -0.060704419
## obese_bmi     -0.0036706272  0.028025616 -0.0062303877 -0.012533132
## concep_spring -0.0079253536 -0.022601581  0.0070452475 -0.019946751
## concep_summer  0.0051091252 -0.005138763  0.0046259743  0.011771877
## concep_fall   -0.0246025662 -0.007565656 -0.0088318656  0.029684511
## concep_2010    0.0083397685 -0.003656536 -0.0087053345  0.010914111
## concep_2011    0.0065695393  0.034722380 -0.0080676182  0.016676703
## concep_2012   -0.0157228628 -0.034872446 -0.0126834700 -0.038431064
## concep_2013    0.0008135550  0.003806601  0.0294564227  0.010840251
## maternal_age   0.1096851777 -0.112036096 -0.0145995420  0.017621395
## any_smoker     0.0088039929  0.048790757  0.0115244458 -0.009662915
## smokeSH       -0.0046810956  0.101925675  0.0056281000 -0.027566686
## mean_cpss      1.0000000000  0.524941092  0.0121083543 -0.032877684
## mean_epsd      0.5249410917  1.000000000 -0.0060537137 -0.078848395
## male           0.0121083543 -0.006053714  0.2504099605 -0.026800015
## gest_age_w    -0.0328776840 -0.078848395 -0.0268000147  1.000000000
ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w, 
                    names_to = "exp", values_to = "value")) + 
    geom_histogram(aes(x = value)) + 
    facet_wrap(~ exp, scales = "free")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

1.3 Response data: birth weight (in grams)

Y <- select(hs_data2, birth_weight) %>%
  as.matrix()
head(Y)
##      birth_weight
## [1,]         3505
## [2,]         2695
## [3,]         3080
## [4,]         3440
## [5,]         3394
## [6,]         3060

Distribution of birth weight and scaled birth weight

hist(Y, breaks = 20)

hist(scale(Y), breaks = 20)

Dropping gest_age_w from the covariates

colnames(W.scaled)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"          "gest_age_w"
W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"

2 RIDGE regression

To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.

set.seed(123)

library(glmnet)
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## Loaded glmnet 4.0-2
lambda_seq <- 10^seq(4, -4, by = -.05)

#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
                      standardize = T, standardize.response = T)
plot(ridge_cv)

best_lambda <- ridge_cv$lambda.min
best_lambda
## [1] 1412.538
#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
                   standardize = T, standardize.response = T)
summary(bw_ridge)
##           Length Class     Mode   
## a0         1     -none-    numeric
## beta      21     dgCMatrix S4     
## df         1     -none-    numeric
## dim        2     -none-    numeric
## lambda     1     -none-    numeric
## dev.ratio  1     -none-    numeric
## nulldev    1     -none-    numeric
## npasses    1     -none-    numeric
## jerr       1     -none-    numeric
## offset     1     -none-    logical
## call       7     -none-    call   
## nobs       1     -none-    numeric

Ridge regression coefficients

coef(bw_ridge)
## 22 x 1 sparse Matrix of class "dgCMatrix"
##                                   s0
## (Intercept)         3527.88072827513
## mean_pm               12.92287834239
## mean_o3               -3.56744503831
## mean_temp             -1.62693356046
## pct_tree_cover        -0.36388972149
## pct_impervious        -0.38915239035
## mean_aadt_intensity   -0.00064476176
## dist_m_tri            -0.00015504654
## dist_m_npl             0.00094355434
## dist_m_waste_site      0.00386069844
## dist_m_major_emit     -0.00022887802
## dist_m_cafo           -0.00001289458
## dist_m_mine_well      -0.00217878564
## cvd_rate_adj           0.01460307637
## res_rate_adj          -0.04961523133
## violent_crime_rate    -0.34399332077
## property_crime_rate   -0.11006094025
## pct_less_hs           -0.83661364882
## pct_unemp             -1.82571596409
## pct_limited_eng       -0.03277560580
## pct_hh_pov            -1.01466481202
## pct_poc                0.06420714355

Ridge regression predictions

ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)

actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))

The R2 value for this model is 0.02. Based on these results, it doesn’t look like there’s much here.

3 Nonparametric Bayesian Shrinkage (NPB): Birth weight

3.1 Finding the NPB priors

3.1.1 Vignette Priors

set.seed(123)

priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 1)

fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects
##       Posterior Mean       SD 95% CI Lower 95% CI Upper   PIP
##  [1,]    0.064024028 2.543619  -0.87540148    0.0000000 0.052
##  [2,]   -0.276967213 6.076312  -2.31592821    0.0000000 0.062
##  [3,]   -0.054355789 2.716440  -1.91194054    0.0000000 0.048
##  [4,]   -0.116003999 1.708604  -2.45222406    0.0000000 0.056
##  [5,]   -0.086183823 1.136087  -0.65445017    0.0000000 0.048
##  [6,]   -0.018782823 2.355395  -1.45280779    0.0000000 0.048
##  [7,]   -0.238014150 2.103096  -3.20257683    0.0000000 0.052
##  [8,]   -0.021394839 1.345509  -1.13858590    0.0000000 0.054
##  [9,]    0.007711504 2.304692   0.00000000    0.0000000 0.034
## [10,]   -0.259099107 2.697696  -4.80388637    0.4523284 0.076
## [11,]   -0.005218549 5.063448  -0.83486231    0.0000000 0.050
## [12,]   -0.217555692 2.274577  -1.45726486    0.0000000 0.048
## [13,]   -0.031911453 1.072786  -0.08358356    0.0000000 0.044
## [14,]   -0.118847360 1.209560  -2.23979385    0.0000000 0.052
## [15,]   -0.299300660 2.324544  -4.50741969    0.0000000 0.048
## [16,]   -0.228573895 1.718744  -3.48895890    0.0000000 0.050
## [17,]   -0.375037028 3.282522  -4.40274535    0.0000000 0.056
## [18,]   -0.393435283 4.048178  -2.72973606    0.0000000 0.062
## [19,]   -0.085530085 1.794808   0.00000000    0.0000000 0.038
## [20,]   -0.138509647 1.384727  -1.45726486    0.0000000 0.052
## [21,]   -0.046301207 1.926945  -0.08358356    0.0000000 0.042
plot(fit.npb.1$beta[,1], type = "l")

plot(fit.npb.1$beta[,2], type = "l")

plot(fit.npb.1$beta[,13], type = "l")

3.1.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10

priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
                     a.phi1 = 10, sig2inv.mu1 = 10)

fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
                 scaleY = TRUE,
                 priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects
##       Posterior Mean        SD 95% CI Lower 95% CI Upper   PIP
##  [1,]      1.7957383 11.481073    -11.64536    33.690294 0.326
##  [2,]     -0.9188404  8.737149    -19.01183    15.001499 0.388
##  [3,]     -0.4102169  7.508868    -16.80982    12.899458 0.314
##  [4,]     -0.5897400  6.442544    -17.72104    12.060223 0.294
##  [5,]     -1.2417945  7.058161    -17.06653    11.333702 0.348
##  [6,]     -1.0077776  5.718843    -15.90191     7.650775 0.322
##  [7,]     -1.9350059  7.197606    -19.62186     7.423318 0.362
##  [8,]     -0.6090866  6.571676    -15.74636    11.658495 0.312
##  [9,]      1.7331228 10.603277    -11.82677    33.043033 0.314
## [10,]     -1.5093281  6.785545    -17.28844     8.687978 0.346
## [11,]      0.1315822 16.683248    -20.37527    34.019055 0.432
## [12,]     -1.7224704  8.093652    -19.98394    10.884684 0.390
## [13,]     -1.2666731  7.309715    -18.11823    10.967504 0.342
## [14,]     -0.4624574  7.833527    -17.43480    13.485397 0.338
## [15,]     -1.7580037  7.104701    -19.01183     7.188367 0.328
## [16,]     -1.9091204  7.134364    -19.41213     6.902233 0.346
## [17,]     -3.7007804 11.623333    -35.87865     6.332795 0.370
## [18,]     -3.2754502  9.445498    -29.31882     4.876851 0.388
## [19,]     -0.5847352  6.535276    -16.89740    11.250882 0.316
## [20,]     -2.1849981  7.766824    -18.65988     4.291485 0.320
## [21,]     -0.4432643  7.217683    -14.03179    13.485397 0.354
plot(fit.npb.24$beta[,1], type = "l")

plot(fit.npb.24$beta[,2], type = "l")

plot(fit.npb.24$beta[,13], type = "l")

3.2 Run the NPB model with temperaure and ozone

Below I’ve used the set of priors labeled “24” and set scaleY = T

The priors are as follows: r priors.npb.24

Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.

priors.npb <- priors.npb.24

#' Exposures 
colnames(X.scaled)
##  [1] "mean_pm"             "mean_o3"             "mean_temp"          
##  [4] "pct_tree_cover"      "pct_impervious"      "mean_aadt_intensity"
##  [7] "dist_m_tri"          "dist_m_npl"          "dist_m_waste_site"  
## [10] "dist_m_major_emit"   "dist_m_cafo"         "dist_m_mine_well"   
## [13] "cvd_rate_adj"        "res_rate_adj"        "violent_crime_rate" 
## [16] "property_crime_rate" "pct_less_hs"         "pct_unemp"          
## [19] "pct_limited_eng"     "pct_hh_pov"          "pct_poc"
#' Covariates
colnames(W.scaled2)
##  [1] "lat"           "lon"           "lat_lon_int"   "ed_no_hs"     
##  [5] "ed_hs"         "ed_aa"         "ed_4yr"        "low_bmi"      
##  [9] "ovwt_bmi"      "obese_bmi"     "concep_spring" "concep_summer"
## [13] "concep_fall"   "concep_2010"   "concep_2011"   "concep_2012"  
## [17] "concep_2013"   "maternal_age"  "any_smoker"    "smokeSH"      
## [21] "mean_cpss"     "mean_epsd"     "male"
# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
#                scaleY = TRUE,
#                priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4b.2.rdata"))

load(here::here("Results", "NPB_Birth_Weight_v4b.2.rdata"))
npb.sum2 <- summary(fit.npb2)

3.2.1 First, main effect regression coefficients with PIPs

rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects
##                     Posterior Mean        SD 95% CI Lower 95% CI Upper    PIP
## mean_pm                1.268902333 10.417098    -14.05244    27.819013 0.3240
## mean_o3               -1.259539645 11.458852    -23.36137    17.622385 0.3464
## mean_temp             -1.069097141 10.241296    -21.98910    14.468908 0.3304
## pct_tree_cover        -0.078352795  7.963849    -15.27524    17.515597 0.3068
## pct_impervious        -1.295749287  7.559532    -20.39060    10.947726 0.3116
## mean_aadt_intensity   -0.948901315  6.696318    -18.73738    11.902765 0.3044
## dist_m_tri            -2.261932420  8.954852    -25.95040     9.679603 0.3544
## dist_m_npl            -0.001456136  8.068803    -14.79201    20.708611 0.2936
## dist_m_waste_site      1.603415112  9.787915    -12.12510    31.900579 0.3300
## dist_m_major_emit     -1.014542477  6.483008    -17.82933    10.168955 0.3108
## dist_m_cafo           -0.345983398 17.922511    -21.95897    24.847532 0.3464
## dist_m_mine_well      -1.774967871  8.530910    -24.07593    12.191663 0.3532
## cvd_rate_adj          -0.962495984  7.750207    -19.08625    13.423337 0.3212
## res_rate_adj          -0.795277915  7.539974    -17.83655    12.090056 0.3024
## violent_crime_rate    -1.074732152  6.787745    -18.71497    11.463321 0.3112
## property_crime_rate   -1.855522242  7.623709    -22.20365     9.666131 0.3152
## pct_less_hs           -2.801052168 10.423547    -30.58982     6.879719 0.3340
## pct_unemp             -2.883291385  9.697163    -29.26122     6.658777 0.3420
## pct_limited_eng       -0.723654955  6.642270    -16.31429    12.382738 0.2992
## pct_hh_pov            -2.392325916  9.287666    -27.35829     8.044338 0.3284
## pct_poc               -0.587480004  6.912553    -16.51112    12.312259 0.2868

3.2.3 Interactions

Next, all of the interactions between exposures or between exposures and covariates

npb.sum2$interactions
##        Posterior Mean         SD 95% CI Lower 95% CI Upper    PIP
##   [1,] -0.00769875041  0.4113312      0.00000       0.0000 0.0040
##   [2,]  0.00059795405  0.4648037      0.00000       0.0000 0.0056
##   [3,] -0.00116448464  0.2891330      0.00000       0.0000 0.0020
##   [4,] -0.03922382107  1.0130056      0.00000       0.0000 0.0056
##   [5,]  0.00695433562  0.4319350      0.00000       0.0000 0.0024
##   [6,] -0.00377542156  0.2844888      0.00000       0.0000 0.0032
##   [7,] -0.00707303850  0.5513934      0.00000       0.0000 0.0052
##   [8,] -0.00220359051  0.3182526      0.00000       0.0000 0.0032
##   [9,] -0.03448487267  1.3064791      0.00000       0.0000 0.0020
##  [10,] -0.07516766149  1.5012843      0.00000       0.0000 0.0064
##  [11,] -0.00052198052  0.3345314      0.00000       0.0000 0.0036
##  [12,] -0.02922020024  0.6183012      0.00000       0.0000 0.0032
##  [13,] -0.06606913784  1.2681853      0.00000       0.0000 0.0052
##  [14,] -0.03924942062  0.8850718      0.00000       0.0000 0.0040
##  [15,] -0.02202960188  0.8344593      0.00000       0.0000 0.0052
##  [16,] -0.02795370625  1.1177482      0.00000       0.0000 0.0028
##  [17,] -0.02181442655  0.9308232      0.00000       0.0000 0.0036
##  [18,] -0.00667802288  0.1891843      0.00000       0.0000 0.0028
##  [19,] -0.02646226893  0.6215589      0.00000       0.0000 0.0048
##  [20,]  0.00387290503  0.7010545      0.00000       0.0000 0.0036
##  [21,] -3.59071228207 16.4943891    -71.36713       0.0000 0.0552
##  [22,] -0.02267297468  0.9395019      0.00000       0.0000 0.0044
##  [23,]  0.02751092439  0.8171618      0.00000       0.0000 0.0040
##  [24,]  0.00433634909  1.0763862      0.00000       0.0000 0.0052
##  [25,] -0.09525744544  1.5400120      0.00000       0.0000 0.0076
##  [26,] -0.01716647783  0.7464236      0.00000       0.0000 0.0012
##  [27,] -0.03323385117  1.0054646      0.00000       0.0000 0.0036
##  [28,] -0.02706674143  0.7555827      0.00000       0.0000 0.0020
##  [29,] -0.01458020986  0.8905581      0.00000       0.0000 0.0024
##  [30,]  0.00436832732  1.0149316      0.00000       0.0000 0.0044
##  [31,] -0.02571826599  0.6407472      0.00000       0.0000 0.0028
##  [32,] -0.00026928601  0.8386506      0.00000       0.0000 0.0040
##  [33,] -0.05801464385  1.1975858      0.00000       0.0000 0.0040
##  [34,]  0.02422294744  0.8765717      0.00000       0.0000 0.0036
##  [35,]  0.01084153388  0.4683559      0.00000       0.0000 0.0044
##  [36,]  0.00401627501  0.2826535      0.00000       0.0000 0.0020
##  [37,]  0.00103926265  0.7364337      0.00000       0.0000 0.0036
##  [38,] -0.01205041575  0.5763760      0.00000       0.0000 0.0032
##  [39,] -0.01877666922  0.5160347      0.00000       0.0000 0.0028
##  [40,] -0.00172290642  0.4470257      0.00000       0.0000 0.0024
##  [41,]  0.00884655761  0.5928049      0.00000       0.0000 0.0036
##  [42,]  0.00512963030  0.3421140      0.00000       0.0000 0.0020
##  [43,] -0.02343539259  0.7157418      0.00000       0.0000 0.0036
##  [44,] -0.01444409844  0.6032739      0.00000       0.0000 0.0012
##  [45,] -0.03543408421  1.1635014      0.00000       0.0000 0.0044
##  [46,] -0.01084450187  0.5449716      0.00000       0.0000 0.0032
##  [47,] -0.04125838892  0.8102235      0.00000       0.0000 0.0056
##  [48,]  0.01688083142  0.4647994      0.00000       0.0000 0.0020
##  [49,]  0.00316499223  0.5228737      0.00000       0.0000 0.0028
##  [50,] -0.00221716063  0.5915823      0.00000       0.0000 0.0032
##  [51,] -0.02308487038  1.0068282      0.00000       0.0000 0.0020
##  [52,]  0.01257276810  0.6875632      0.00000       0.0000 0.0024
##  [53,] -0.01750359469  0.4064495      0.00000       0.0000 0.0028
##  [54,]  0.02413723652  1.0714316      0.00000       0.0000 0.0044
##  [55,] -0.00329019626  0.2474231      0.00000       0.0000 0.0028
##  [56,] -0.01589765178  0.5821814      0.00000       0.0000 0.0040
##  [57,] -0.10488148399  2.2586867      0.00000       0.0000 0.0040
##  [58,]  0.00871811926  0.5270382      0.00000       0.0000 0.0024
##  [59,] -0.01356962488  0.6164354      0.00000       0.0000 0.0036
##  [60,] -0.00789397624  0.4177318      0.00000       0.0000 0.0040
##  [61,] -0.01275086237  0.7516430      0.00000       0.0000 0.0040
##  [62,] -0.00496959562  0.5218589      0.00000       0.0000 0.0032
##  [63,]  0.02082593758  0.8849207      0.00000       0.0000 0.0044
##  [64,] -0.01875696329  0.9487662      0.00000       0.0000 0.0044
##  [65,] -0.05840666038  1.8586991      0.00000       0.0000 0.0028
##  [66,]  0.00424914303  0.5621072      0.00000       0.0000 0.0028
##  [67,] -0.00835179990  1.1677522      0.00000       0.0000 0.0036
##  [68,] -0.01559677137  0.5417615      0.00000       0.0000 0.0024
##  [69,] -0.00594780402  0.3684520      0.00000       0.0000 0.0024
##  [70,] -0.00863662383  0.7657188      0.00000       0.0000 0.0032
##  [71,] -0.02917118398  0.8516269      0.00000       0.0000 0.0048
##  [72,] -0.05970716158  1.4864187      0.00000       0.0000 0.0036
##  [73,] -0.02614120733  0.8678491      0.00000       0.0000 0.0036
##  [74,] -0.00751725130  0.6151958      0.00000       0.0000 0.0024
##  [75,]  0.00388314888  0.6159567      0.00000       0.0000 0.0044
##  [76,]  0.02663240510  0.8602454      0.00000       0.0000 0.0024
##  [77,] -0.01941697589  0.6503672      0.00000       0.0000 0.0032
##  [78,]  0.00597836429  0.4870830      0.00000       0.0000 0.0032
##  [79,] -0.01113481480  0.5242877      0.00000       0.0000 0.0032
##  [80,] -0.02263250605  0.6677566      0.00000       0.0000 0.0024
##  [81,] -0.00299188357  0.5298071      0.00000       0.0000 0.0036
##  [82,] -0.03705124758  0.8898507      0.00000       0.0000 0.0064
##  [83,] -0.03213772102  0.7172030      0.00000       0.0000 0.0044
##  [84,]  0.00224175546  0.5823033      0.00000       0.0000 0.0040
##  [85,] -0.00512550857  0.3101711      0.00000       0.0000 0.0028
##  [86,] -0.00167504716  0.3390186      0.00000       0.0000 0.0024
##  [87,] -0.03645031281  0.9906775      0.00000       0.0000 0.0036
##  [88,] -0.00651842228  1.0232513      0.00000       0.0000 0.0028
##  [89,] -0.03381804419  0.8363009      0.00000       0.0000 0.0048
##  [90,]  0.00053788729  0.3452219      0.00000       0.0000 0.0040
##  [91,]  0.03197251797  1.7615557      0.00000       0.0000 0.0036
##  [92,] -0.00203364747  0.4531471      0.00000       0.0000 0.0024
##  [93,]  0.00480344876  0.3092560      0.00000       0.0000 0.0024
##  [94,] -0.00729841981  0.3807151      0.00000       0.0000 0.0040
##  [95,] -0.07078591739  1.8739084      0.00000       0.0000 0.0052
##  [96,] -0.01246886925  1.3550782      0.00000       0.0000 0.0040
##  [97,] -0.03720006024  0.8005706      0.00000       0.0000 0.0052
##  [98,] -0.00417808806  0.1892680      0.00000       0.0000 0.0028
##  [99,] -0.01393404154  0.8798002      0.00000       0.0000 0.0048
## [100,] -0.04242206529  0.9743912      0.00000       0.0000 0.0036
## [101,] -0.01972463216  1.3081597      0.00000       0.0000 0.0036
## [102,] -0.01357065469  0.5375590      0.00000       0.0000 0.0032
## [103,]  0.01700674207  1.1041724      0.00000       0.0000 0.0036
## [104,]  0.01810342837  0.6043164      0.00000       0.0000 0.0028
## [105,]  0.01524952190  1.0551326      0.00000       0.0000 0.0036
## [106,]  0.00375803843  0.6029684      0.00000       0.0000 0.0048
## [107,] -0.04946471231  1.4407593      0.00000       0.0000 0.0040
## [108,] -0.03656088329  0.9154608      0.00000       0.0000 0.0044
## [109,] -0.00782978789  0.2563507      0.00000       0.0000 0.0024
## [110,] -0.02752008565  0.6992245      0.00000       0.0000 0.0044
## [111,] -0.00223132766  1.1376129      0.00000       0.0000 0.0036
## [112,]  0.00937149086  0.4946252      0.00000       0.0000 0.0044
## [113,] -0.01793433864  0.5950490      0.00000       0.0000 0.0044
## [114,] -0.00404355176  1.0221689      0.00000       0.0000 0.0044
## [115,]  0.00077647028  0.6394007      0.00000       0.0000 0.0064
## [116,] -0.02418627669  0.9115807      0.00000       0.0000 0.0032
## [117,] -0.00728812158  0.5226746      0.00000       0.0000 0.0024
## [118,]  0.01117871509  0.6380531      0.00000       0.0000 0.0024
## [119,]  0.00437065387  0.4148449      0.00000       0.0000 0.0032
## [120,] -0.00175017509  0.5497240      0.00000       0.0000 0.0048
## [121,] -0.00174963754  0.5759413      0.00000       0.0000 0.0032
## [122,] -0.02367602200  0.7360187      0.00000       0.0000 0.0036
## [123,] -0.01110691857  0.4854675      0.00000       0.0000 0.0040
## [124,]  0.00978407957  0.5831135      0.00000       0.0000 0.0036
## [125,]  0.00331844316  0.7907854      0.00000       0.0000 0.0032
## [126,]  0.03683024975  1.6637564      0.00000       0.0000 0.0052
## [127,]  0.01088696547  0.5628425      0.00000       0.0000 0.0064
## [128,]  0.01436414268  1.0079007      0.00000       0.0000 0.0044
## [129,]  0.00174970969  0.5873818      0.00000       0.0000 0.0036
## [130,]  0.01457738648  0.8872264      0.00000       0.0000 0.0040
## [131,] -0.00717487502  0.4356942      0.00000       0.0000 0.0036
## [132,]  0.00340049241  0.2742816      0.00000       0.0000 0.0016
## [133,]  0.00410649914  0.2367491      0.00000       0.0000 0.0024
## [134,]  0.02740458433  0.9602859      0.00000       0.0000 0.0036
## [135,] -0.03099307390  1.1349281      0.00000       0.0000 0.0032
## [136,] -0.00058867876  0.6721599      0.00000       0.0000 0.0048
## [137,]  0.02271730534  0.9885975      0.00000       0.0000 0.0048
## [138,] -0.00298908104  0.2736734      0.00000       0.0000 0.0012
## [139,] -0.00495243713  0.4582808      0.00000       0.0000 0.0024
## [140,] -0.00739582165  0.8156671      0.00000       0.0000 0.0040
## [141,] -0.00036011661  0.6702937      0.00000       0.0000 0.0028
## [142,]  0.00962373962  0.7903291      0.00000       0.0000 0.0048
## [143,]  0.02490657919  1.0421145      0.00000       0.0000 0.0040
## [144,] -0.01261237777  0.5042105      0.00000       0.0000 0.0028
## [145,]  0.03905372388  1.1683810      0.00000       0.0000 0.0040
## [146,] -0.01185756590  0.6266944      0.00000       0.0000 0.0020
## [147,] -0.01895345667  0.5554110      0.00000       0.0000 0.0040
## [148,] -0.02534595285  0.6722204      0.00000       0.0000 0.0020
## [149,] -0.00002276072  0.3724896      0.00000       0.0000 0.0028
## [150,]  0.00483145056  0.3798442      0.00000       0.0000 0.0036
## [151,] -0.18879686754  2.8219088      0.00000       0.0000 0.0092
## [152,]  0.00360155511  0.3867350      0.00000       0.0000 0.0024
## [153,] -0.00904404795  0.5793905      0.00000       0.0000 0.0044
## [154,]  0.00363809775  0.6791680      0.00000       0.0000 0.0040
## [155,] -0.00452774284  0.3540227      0.00000       0.0000 0.0032
## [156,] -0.02281342820  0.6031122      0.00000       0.0000 0.0044
## [157,]  0.01200960861  1.5624979      0.00000       0.0000 0.0044
## [158,] -0.01870770721  1.4831459      0.00000       0.0000 0.0060
## [159,] -0.01200346985  0.6540867      0.00000       0.0000 0.0028
## [160,] -0.01115456386  0.5729364      0.00000       0.0000 0.0032
## [161,] -0.00641048910  0.5500546      0.00000       0.0000 0.0040
## [162,]  0.00621373045  0.3784975      0.00000       0.0000 0.0020
## [163,]  0.01628914857  0.9426373      0.00000       0.0000 0.0036
## [164,]  0.01804730047  0.7131631      0.00000       0.0000 0.0028
## [165,]  0.05266605348  1.8002611      0.00000       0.0000 0.0052
## [166,]  0.01703977184  0.7087822      0.00000       0.0000 0.0024
## [167,] -0.00373575530  0.4208188      0.00000       0.0000 0.0032
## [168,] -0.04405844374  1.1075009      0.00000       0.0000 0.0040
## [169,] -0.01448859618  0.8364060      0.00000       0.0000 0.0044
## [170,]  0.01883397484  1.1503957      0.00000       0.0000 0.0048
## [171,] -0.00997013348  0.7314178      0.00000       0.0000 0.0040
## [172,] -0.02598923852  1.1868592      0.00000       0.0000 0.0028
## [173,]  0.04367184807  1.4926297      0.00000       0.0000 0.0028
## [174,] -0.05268959095  1.7534438      0.00000       0.0000 0.0044
## [175,] -0.05200945526  0.9415618      0.00000       0.0000 0.0056
## [176,] -0.01727545176  0.4635505      0.00000       0.0000 0.0040
## [177,] -0.03587948516  0.8368013      0.00000       0.0000 0.0044
## [178,] -0.02999418358  0.7145021      0.00000       0.0000 0.0024
## [179,] -0.02272834909  0.5090716      0.00000       0.0000 0.0032
## [180,] -0.01674630174  0.4462596      0.00000       0.0000 0.0032
## [181,] -0.04197311474  1.0318319      0.00000       0.0000 0.0052
## [182,] -0.03412124905  0.8977085      0.00000       0.0000 0.0028
## [183,] -0.01025336733  0.5792840      0.00000       0.0000 0.0032
## [184,] -0.01052273013  0.4268502      0.00000       0.0000 0.0040
## [185,] -0.01959676037  0.5179252      0.00000       0.0000 0.0032
## [186,] -0.02141415729  0.8062161      0.00000       0.0000 0.0048
## [187,] -0.02777187524  1.1995210      0.00000       0.0000 0.0032
## [188,] -0.34908493768  3.9878503      0.00000       0.0000 0.0112
## [189,] -0.02222920369  0.7028515      0.00000       0.0000 0.0040
## [190,] -0.01030996074  0.2656684      0.00000       0.0000 0.0028
## [191,]  0.01119002259  0.6556281      0.00000       0.0000 0.0052
## [192,] -0.02757861068  1.0353054      0.00000       0.0000 0.0036
## [193,]  0.01444198533  0.5765084      0.00000       0.0000 0.0024
## [194,] -0.05301378460  1.1869155      0.00000       0.0000 0.0060
## [195,] -0.01871813914  0.5784420      0.00000       0.0000 0.0032
## [196,] -0.03982361609  0.9074604      0.00000       0.0000 0.0052
## [197,] -0.00301182808  0.4485023      0.00000       0.0000 0.0028
## [198,]  0.00390441720  0.9958726      0.00000       0.0000 0.0048
## [199,] -0.10627373863  2.2052971      0.00000       0.0000 0.0052
## [200,] -0.00604555308  0.5956815      0.00000       0.0000 0.0024
## [201,] -0.00102920945  0.5079239      0.00000       0.0000 0.0036
## [202,] -0.01251379188  0.4179332      0.00000       0.0000 0.0040
## [203,] -0.01405800645  0.4999416      0.00000       0.0000 0.0028
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## [220,]  0.00095377490  0.3998620      0.00000       0.0000 0.0040
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## [267,] -0.56743039943 11.5285946      0.00000       0.0000 0.0068
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## [269,]  8.71589666955 45.1378887      0.00000     197.0717 0.0440
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## [271,] -0.03364161929  1.2002871      0.00000       0.0000 0.0040
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## [276,] -0.03927092733  1.0548663      0.00000       0.0000 0.0044
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## [278,] -0.02337076940  0.7581235      0.00000       0.0000 0.0036
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## [280,]  0.00901750534  0.4806154      0.00000       0.0000 0.0028
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## [283,]  0.34982031105  8.4465912      0.00000       0.0000 0.0052
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## [285,] -0.04058589110  1.1359411      0.00000       0.0000 0.0044
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## [288,] -0.04794287958  1.0986589      0.00000       0.0000 0.0056
## [289,]  0.00599946257  1.1059167      0.00000       0.0000 0.0032
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## [305,] -0.01220772992  0.6438844      0.00000       0.0000 0.0040
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## [310,] -0.27474233750  7.1713862      0.00000       0.0000 0.0032
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## [313,]  0.01496636603  1.7646321      0.00000       0.0000 0.0036
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## [315,] -0.04246105969  1.2479416      0.00000       0.0000 0.0044
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## [324,] -0.00582492334  0.5241017      0.00000       0.0000 0.0032
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## [449,] -0.13136742707  3.4144321      0.00000       0.0000 0.0068
## [450,]  0.02140194646  0.8556762      0.00000       0.0000 0.0040
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## [457,] -0.03307245138  1.9865025      0.00000       0.0000 0.0048
## [458,] -0.00386691320  0.4361660      0.00000       0.0000 0.0032
## [459,] -0.04175794055  4.2695099      0.00000       0.0000 0.0044
## [460,]  0.02525850757  2.9543864      0.00000       0.0000 0.0056
## [461,]  0.00331686103  0.6656359      0.00000       0.0000 0.0032
## [462,] -0.01492941458  1.1260497      0.00000       0.0000 0.0048
## [463,] -0.02052709255  0.6752604      0.00000       0.0000 0.0052
## [464,] -0.00506947629  0.2970605      0.00000       0.0000 0.0012
## [465,]  0.00851614388  0.5236066      0.00000       0.0000 0.0032
## [466,] -0.07618214007  1.6006329      0.00000       0.0000 0.0056
## [467,]  0.01680303258  1.0638035      0.00000       0.0000 0.0024
## [468,] -0.05515923928  1.7083281      0.00000       0.0000 0.0072
## [469,] -0.05418377145  1.8068848      0.00000       0.0000 0.0044
## [470,] -0.00849203885  0.8020599      0.00000       0.0000 0.0044
## [471,]  0.14505689781  6.6450690      0.00000       0.0000 0.0048
## [472,] -0.00046107186  0.6389301      0.00000       0.0000 0.0040
## [473,]  0.03201694802  1.1030427      0.00000       0.0000 0.0040
## [474,] -0.00363609412  0.4737074      0.00000       0.0000 0.0040
## [475,] -0.12978661043  2.6213611      0.00000       0.0000 0.0044
## [476,] -0.01715904918  1.3057326      0.00000       0.0000 0.0048
## [477,] -0.01839170075  0.7218551      0.00000       0.0000 0.0036
## [478,]  0.03150496826  1.4975485      0.00000       0.0000 0.0048
## [479,] -0.22566238089  3.6082015      0.00000       0.0000 0.0092
## [480,]  0.00467218560  0.7066024      0.00000       0.0000 0.0036
## [481,] -0.00069287807  0.4751221      0.00000       0.0000 0.0040
## [482,] -0.16995316614  4.4771007      0.00000       0.0000 0.0084
## [483,] -0.02137437150  1.2022203      0.00000       0.0000 0.0020
## [484,] -0.02424372231  0.8308607      0.00000       0.0000 0.0052
## [485,]  0.01943375577  0.8106759      0.00000       0.0000 0.0032
## [486,] -0.03002148512  1.0338628      0.00000       0.0000 0.0040
## [487,] -0.02898787124  0.9602734      0.00000       0.0000 0.0068
## [488,] -0.03856074551  1.2911913      0.00000       0.0000 0.0028
## [489,]  0.00323675888  0.1836902      0.00000       0.0000 0.0036
## [490,]  0.07572680687  4.0426992      0.00000       0.0000 0.0052
## [491,]  0.11329226180  4.7810903      0.00000       0.0000 0.0044
## [492,]  1.42923787241 16.3996905      0.00000       0.0000 0.0128
## [493,] -0.13399865318  2.8146073      0.00000       0.0000 0.0072
## [494,] -0.04794318973  1.9910474      0.00000       0.0000 0.0072
## [495,]  0.01829751919  1.0566572      0.00000       0.0000 0.0040
## [496,]  0.01819159982  0.7976391      0.00000       0.0000 0.0040
## [497,]  0.00355098721  1.2030169      0.00000       0.0000 0.0044
## [498,] -0.01920935812  1.5851391      0.00000       0.0000 0.0064
## [499,] -0.13128225467  3.5921239      0.00000       0.0000 0.0040
## [500,] -0.29360444004  4.8432256      0.00000       0.0000 0.0076
## [501,]  0.00653440759  0.9854360      0.00000       0.0000 0.0028
## [502,]  0.43943113961  7.5306760      0.00000       0.0000 0.0068
## [503,] -0.13144509082  3.1739267      0.00000       0.0000 0.0040
## [504,]  0.01515919611  0.7401277      0.00000       0.0000 0.0028
## [505,] -0.06726171533  2.4484431      0.00000       0.0000 0.0044
## [506,]  0.01769896011  0.9269617      0.00000       0.0000 0.0060
## [507,]  0.00183040186  0.1326357      0.00000       0.0000 0.0016
## [508,]  0.02284480380  0.8273465      0.00000       0.0000 0.0036
## [509,] -0.02829557874  1.5644437      0.00000       0.0000 0.0044
## [510,] -0.04284039577  1.2892193      0.00000       0.0000 0.0032
## [511,]  0.00357223459  0.5032942      0.00000       0.0000 0.0028
## [512,]  0.00354449681  0.4610170      0.00000       0.0000 0.0040
## [513,]  0.00366040350  6.5772971      0.00000       0.0000 0.0068
## [514,]  0.10025662025  4.1447237      0.00000       0.0000 0.0044
## [515,] 25.25037537901 73.9572817      0.00000     266.9447 0.1164
## [516,] -0.06694221375  1.6130936      0.00000       0.0000 0.0044
## [517,] -0.14196601596  4.8430170      0.00000       0.0000 0.0052
## [518,] -0.00308493565  1.1392973      0.00000       0.0000 0.0048
## [519,] -0.05611687967  1.3755533      0.00000       0.0000 0.0024
## [520,] -0.03927029703  1.2675289      0.00000       0.0000 0.0060
## [521,]  0.00222983117  0.5424910      0.00000       0.0000 0.0032
## [522,] -0.03964003966  1.3749273      0.00000       0.0000 0.0036
## [523,] -0.06926051823  2.8090081      0.00000       0.0000 0.0036
## [524,]  0.00835894428  1.1934139      0.00000       0.0000 0.0036
## [525,]  0.03621586774  1.9267808      0.00000       0.0000 0.0044
## [526,] -0.05122755753  1.6540809      0.00000       0.0000 0.0048
## [527,]  0.00094735321  0.7810354      0.00000       0.0000 0.0044
## [528,] -0.05606194311  1.7079614      0.00000       0.0000 0.0036
## [529,]  0.00963400254  1.0270840      0.00000       0.0000 0.0076
## [530,]  0.01016243164  0.4757702      0.00000       0.0000 0.0060
## [531,]  0.02992124272  0.8312102      0.00000       0.0000 0.0028
## [532,] -0.08775179795  2.5027649      0.00000       0.0000 0.0056
## [533,]  0.00043632094  1.2268502      0.00000       0.0000 0.0072
## [534,]  0.00580146997  0.4474064      0.00000       0.0000 0.0024
## [535,] -0.00034946383  0.4085513      0.00000       0.0000 0.0024
## [536,] -0.02137281009  1.7270183      0.00000       0.0000 0.0044
## [537,]  0.26694273350  7.6647911      0.00000       0.0000 0.0060
## [538,] -0.04376338119  1.8644821      0.00000       0.0000 0.0036
## [539,] -0.13620057804  2.5474464      0.00000       0.0000 0.0052
## [540,] -0.08953476343  3.7312823      0.00000       0.0000 0.0068
## [541,] -0.09131545902  2.3726982      0.00000       0.0000 0.0064
## [542,]  0.03906997285  1.2353138      0.00000       0.0000 0.0044
## [543,]  0.02047090922  1.0779427      0.00000       0.0000 0.0032
## [544,]  0.00055388071  0.6681001      0.00000       0.0000 0.0056
## [545,]  0.04302223578  2.7292821      0.00000       0.0000 0.0056
## [546,] -0.05660307001  1.7090770      0.00000       0.0000 0.0036
## [547,]  0.00006248598  0.5008925      0.00000       0.0000 0.0028
## [548,] -0.00723005275  0.3501476      0.00000       0.0000 0.0024
## [549,]  0.05426827983  2.9132422      0.00000       0.0000 0.0040
## [550,]  0.05300683774  1.3531919      0.00000       0.0000 0.0036
## [551,] -0.03159046107  1.1513509      0.00000       0.0000 0.0036
## [552,] -0.03945277984  0.9687489      0.00000       0.0000 0.0044
## [553,] -0.01860407413  0.4403944      0.00000       0.0000 0.0032
## [554,] -0.01088386718  0.5578712      0.00000       0.0000 0.0032
## [555,] -0.00095585553  0.6231777      0.00000       0.0000 0.0052
## [556,]  0.00677413013  1.1756924      0.00000       0.0000 0.0044
## [557,]  0.00021787249  0.9477142      0.00000       0.0000 0.0032
## [558,] -0.00115629761  0.1256469      0.00000       0.0000 0.0012
## [559,] -0.02578391886  7.4291035      0.00000       0.0000 0.0064
## [560,]  0.05809806076  5.4658690      0.00000       0.0000 0.0048
## [561,] -0.04820797757  1.6637725      0.00000       0.0000 0.0028
## [562,] -0.06885141438  2.1389151      0.00000       0.0000 0.0032
## [563,] -0.14436983259  6.6060006      0.00000       0.0000 0.0052
## [564,]  0.00142543336  0.2946349      0.00000       0.0000 0.0016
## [565,]  0.00093104590  0.6004580      0.00000       0.0000 0.0036
## [566,] -0.01144459633  0.6020731      0.00000       0.0000 0.0044
## [567,] -0.08474550600  2.2934677      0.00000       0.0000 0.0036
## [568,] -0.03326796372  1.5353455      0.00000       0.0000 0.0044
## [569,] -0.04559651458  2.0226149      0.00000       0.0000 0.0064
## [570,]  0.02488196339  1.7384842      0.00000       0.0000 0.0072
## [571,] -0.02033233804  1.1427616      0.00000       0.0000 0.0040
## [572,] -0.04137063693  1.3557754      0.00000       0.0000 0.0036
## [573,] -0.00704169146  0.5367890      0.00000       0.0000 0.0036
## [574,]  0.14080183513 12.2076152      0.00000       0.0000 0.0052
## [575,] -0.03019195427  0.8217134      0.00000       0.0000 0.0024
## [576,] -0.17607913139  3.5555915      0.00000       0.0000 0.0068
## [577,] -0.01696603560  0.4776077      0.00000       0.0000 0.0032
## [578,] -0.02704320435  1.6266095      0.00000       0.0000 0.0044
## [579,] -0.09462526904  2.0402393      0.00000       0.0000 0.0064
## [580,] -0.07681748969  2.0066045      0.00000       0.0000 0.0060
## [581,] -0.00581490046  0.4423204      0.00000       0.0000 0.0040
## [582,] -0.02606931502  1.7931706      0.00000       0.0000 0.0048
## [583,] -0.02702163895  0.6713354      0.00000       0.0000 0.0052
## [584,] -0.01842901049  0.7218367      0.00000       0.0000 0.0040
## [585,] -0.15872977084  3.2080013      0.00000       0.0000 0.0060
## [586,]  0.08389018469  3.6039164      0.00000       0.0000 0.0016
## [587,]  0.00038806967  0.3672994      0.00000       0.0000 0.0032
## [588,] -0.25795439273  5.1353457      0.00000       0.0000 0.0068
## [589,] -0.48608457583  7.6498739      0.00000       0.0000 0.0088
## [590,] -0.00802561687  0.4227186      0.00000       0.0000 0.0044
## [591,] -0.04024175896  1.4416101      0.00000       0.0000 0.0020
## [592,]  0.05991073884  2.9831163      0.00000       0.0000 0.0040
## [593,] -0.09934179787  2.1042539      0.00000       0.0000 0.0044
## [594,] -0.01221089429  0.6211732      0.00000       0.0000 0.0044
## [595,] -0.09728793260  2.8910277      0.00000       0.0000 0.0056
## [596,] -0.02357146205  0.5400814      0.00000       0.0000 0.0028
## [597,] -0.03769460606  1.8298453      0.00000       0.0000 0.0060
## [598,]  0.03722744017  2.5259169      0.00000       0.0000 0.0052
## [599,] -0.01403809899  0.6955268      0.00000       0.0000 0.0028
## [600,] -0.00279151472  0.3384934      0.00000       0.0000 0.0036
## [601,] -0.34230966147  4.7906850      0.00000       0.0000 0.0100
## [602,] -0.01512593870  0.5582302      0.00000       0.0000 0.0052
## [603,] -0.02037469408  0.8883290      0.00000       0.0000 0.0056
## [604,] -0.00939840080  0.4845240      0.00000       0.0000 0.0048
## [605,]  0.00549360618  0.4381474      0.00000       0.0000 0.0020
## [606,]  0.40729559966  8.7120614      0.00000       0.0000 0.0048
## [607,] -0.03603302394  1.3762765      0.00000       0.0000 0.0052
## [608,] -1.63058258413 13.3994865      0.00000       0.0000 0.0220
## [609,] -0.02700141747  1.3612281      0.00000       0.0000 0.0044
## [610,] -0.04868388185  1.4625255      0.00000       0.0000 0.0028
## [611,] -0.05502920798  1.3940249      0.00000       0.0000 0.0068
## [612,] -0.05408136219  1.7040516      0.00000       0.0000 0.0036
## [613,] -0.02740444379  0.7505288      0.00000       0.0000 0.0040
## [614,] -0.00561482463  1.0083766      0.00000       0.0000 0.0056
## [615,] -0.02004677999  1.4795313      0.00000       0.0000 0.0024
## [616,] -0.12913689552  3.4252177      0.00000       0.0000 0.0056
## [617,]  0.02325429239  1.1302185      0.00000       0.0000 0.0048
## [618,] -0.12025295677  3.0700794      0.00000       0.0000 0.0040
## [619,] -0.05009662903  1.5926231      0.00000       0.0000 0.0028
## [620,] -0.09141923437  3.1969494      0.00000       0.0000 0.0048
## [621,] -0.06350196597  1.9593231      0.00000       0.0000 0.0044
## [622,]  0.00839579421  0.3080303      0.00000       0.0000 0.0032
## [623,]  0.00084266129  0.6312353      0.00000       0.0000 0.0052
## [624,] -0.36342270793  5.5362577      0.00000       0.0000 0.0100
## [625,] -0.08043972691  1.6784085      0.00000       0.0000 0.0068
## [626,] -0.02184861268  1.2489367      0.00000       0.0000 0.0040
## [627,]  0.01715453739  0.8804932      0.00000       0.0000 0.0032
## [628,] -0.00994879841  1.1322588      0.00000       0.0000 0.0028
## [629,] -0.01328127933  1.0050553      0.00000       0.0000 0.0036
## [630,] -0.00927151182  0.7166267      0.00000       0.0000 0.0028
## [631,] -0.00738518217  1.6527724      0.00000       0.0000 0.0068
## [632,] -0.00106871768  0.1265114      0.00000       0.0000 0.0024
## [633,] -0.02301030672  1.2726529      0.00000       0.0000 0.0080
## [634,] -0.04930495560  1.3778623      0.00000       0.0000 0.0052
## [635,] -0.05782478230  1.4320141      0.00000       0.0000 0.0044
## [636,] -0.00058011961  1.0826969      0.00000       0.0000 0.0020
## [637,]  0.05187755550  2.4821179      0.00000       0.0000 0.0040
## [638,] -0.01120569630  0.5420322      0.00000       0.0000 0.0036
## [639,] -0.04786985142  1.2028871      0.00000       0.0000 0.0064
## [640,]  0.01378020588  1.1902183      0.00000       0.0000 0.0044
## [641,] -0.00827690405  0.5285552      0.00000       0.0000 0.0040
## [642,] -0.02179855209  0.9380286      0.00000       0.0000 0.0040
## [643,] -0.02636909075  0.9334187      0.00000       0.0000 0.0060
## [644,] -0.00489087889  1.0321457      0.00000       0.0000 0.0040
## [645,] -0.00718481339  0.4985295      0.00000       0.0000 0.0020
## [646,]  0.01391585731  0.5376600      0.00000       0.0000 0.0040
## [647,] -0.02144296210  0.6852352      0.00000       0.0000 0.0052
## [648,] -0.02107174174  0.7242061      0.00000       0.0000 0.0036
## [649,] -0.00635279710  0.4149004      0.00000       0.0000 0.0032
## [650,]  0.01076489108  0.7802904      0.00000       0.0000 0.0036
## [651,] -0.03712005318  1.3418039      0.00000       0.0000 0.0036
## [652,] -0.00764874157  0.5726982      0.00000       0.0000 0.0036
## [653,] -0.04494232280  1.7145491      0.00000       0.0000 0.0024
## [654,] -0.01654217210  0.9977905      0.00000       0.0000 0.0048
## [655,] -0.16076937682  4.3320576      0.00000       0.0000 0.0064
## [656,] -0.05190527333  1.2671586      0.00000       0.0000 0.0036
## [657,] -0.02551092536  0.9270217      0.00000       0.0000 0.0032
## [658,] -0.06570075369  2.2272467      0.00000       0.0000 0.0032
## [659,] -0.00502617813  0.3052554      0.00000       0.0000 0.0012
## [660,]  0.01032296252  0.4043590      0.00000       0.0000 0.0016
## [661,] -0.06642314875  2.5078787      0.00000       0.0000 0.0060
## [662,] -0.03356336954  1.0062210      0.00000       0.0000 0.0052
## [663,]  0.05625419349  2.0628764      0.00000       0.0000 0.0040
## [664,] -0.01245983636  0.6697871      0.00000       0.0000 0.0044
## [665,] -0.00845625132  0.4204365      0.00000       0.0000 0.0032
## [666,]  0.01168857255  2.1705254      0.00000       0.0000 0.0048
## [667,] -0.03142183555  1.5140836      0.00000       0.0000 0.0028
## [668,] -0.01995430455  0.5408620      0.00000       0.0000 0.0024
## [669,]  0.00433839071  0.7119034      0.00000       0.0000 0.0068
## [670,] -0.26667541472  4.3068049      0.00000       0.0000 0.0084
## [671,] -0.02803173467  1.4835196      0.00000       0.0000 0.0048
## [672,]  0.00101337570  0.4256440      0.00000       0.0000 0.0040
## [673,]  0.02990345868  1.0160220      0.00000       0.0000 0.0040
## [674,] -0.05968635033  1.4501770      0.00000       0.0000 0.0052
## [675,] -0.00495262520  0.1776880      0.00000       0.0000 0.0024
## [676,] -0.01569551812  1.4021773      0.00000       0.0000 0.0048
## [677,] -0.06826071069  2.1210282      0.00000       0.0000 0.0056
## [678,] -0.09455256251  2.6717979      0.00000       0.0000 0.0064
## [679,]  0.07258164237  2.3456410      0.00000       0.0000 0.0040
## [680,] -0.06158137459  1.7814387      0.00000       0.0000 0.0040
## [681,] -0.03223576531  2.0473225      0.00000       0.0000 0.0040
## [682,]  0.04720113571  2.4969594      0.00000       0.0000 0.0048
## [683,]  0.01687818378  0.4608714      0.00000       0.0000 0.0032
## [684,] -0.05212446226  2.4020504      0.00000       0.0000 0.0040
## [685,]  0.00257794645  0.5989752      0.00000       0.0000 0.0032
## [686,]  0.22471634305  5.5725886      0.00000       0.0000 0.0084
## [687,] -0.05690365650  2.0806055      0.00000       0.0000 0.0032
## [688,] -0.00441251512  0.4018209      0.00000       0.0000 0.0032
## [689,] -0.05993846525  2.1765355      0.00000       0.0000 0.0040
## [690,] -0.01441780180  0.5942107      0.00000       0.0000 0.0020
## [691,] -0.01958745926  0.7149677      0.00000       0.0000 0.0028
## [692,]  0.00628593521  0.3077307      0.00000       0.0000 0.0016
## [693,] -0.06516600345  1.6650428      0.00000       0.0000 0.0052

3.2.4 Predict fitted values for each individual

pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals

3.2.5 Plot predicted outcomes against “measured” outcomes

plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")

4 Linear models for each predictor

4.1 Screening the exposures

Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.

The standard deviation of the mean_o3 variable is 2.98 ppb

lm_results <- data.frame()

for(i in 1:length(colnames(X.scaled))) {
  lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
  names(lm_df)[2] <- colnames(X.scaled)[i]
  
  ad_lm <- lm(birth_weight ~ ., data = lm_df)
  
  temp <- data.frame(exp = colnames(X.scaled)[i],
                     beta = summary(ad_lm)$coefficients[2,1],
                     beta.se = summary(ad_lm)$coefficients[2,2],
                     p.value = summary(ad_lm)$coefficients[2,4])
  temp$lcl <- temp$beta - 1.96*temp$beta.se
  temp$ucl <- temp$beta + 1.96*temp$beta.se
  lm_results <- bind_rows(lm_results, temp)
  rm(temp)
}

lm_results
write_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4b.csv"))

5 Linear model with the ozone and temperature predictors

The standard deviation of the mean_o3 variable is 2.98 ppb The standard deviation of the mean_temp variable is 4.39 degrees F

lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
#names(lm_df)[2] <- "mean_o3"

head(lm_df)
bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
              lat + lon + lat_lon_int +
              ed_no_hs + ed_hs + ed_aa + ed_4yr + 
              low_bmi + ovwt_bmi + obese_bmi + 
              concep_spring + concep_summer + concep_fall +
              concep_2010 + concep_2011 + concep_2012 + concep_2013 +
              maternal_age + any_smoker + smokeSH + 
              mean_cpss + mean_epsd + male,
              data = lm_df)

summary(bw_lm)
## 
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp + 
##     lat + lon + lat_lon_int + ed_no_hs + ed_hs + ed_aa + ed_4yr + 
##     low_bmi + ovwt_bmi + obese_bmi + concep_spring + concep_summer + 
##     concep_fall + concep_2010 + concep_2011 + concep_2012 + concep_2013 + 
##     maternal_age + any_smoker + smokeSH + mean_cpss + mean_epsd + 
##     male, data = lm_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2098.72  -304.96    12.59   329.55  1142.03 
## 
## Coefficients: (1 not defined because of singularities)
##                     Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)        3327.6603    87.5116  38.025 < 0.0000000000000002 ***
## mean_o3             -25.2753    70.7784  -0.357             0.721193    
## mean_temp            33.1198    68.7757   0.482             0.630368    
## lat                 594.1046 24436.0007   0.024             0.980615    
## lon                -229.7916 11503.6831  -0.020             0.984072    
## lat_lon_int         731.6944 29742.5406   0.025             0.980385    
## ed_no_hs             63.9484   141.0645   0.453             0.650548    
## ed_hs                -4.0768   105.0427  -0.039             0.969060    
## ed_aa                60.8840    77.1412   0.789             0.430410    
## ed_4yr               43.9070    55.4575   0.792             0.428970    
## low_bmi            -179.1352   130.6846  -1.371             0.171188    
## ovwt_bmi            -20.3753    56.9547  -0.358             0.720713    
## obese_bmi            90.4497    70.8873   1.276             0.202675    
## concep_spring       -23.4264    81.4981  -0.287             0.773912    
## concep_summer        41.0057   109.5242   0.374             0.708297    
## concep_fall         130.5375   105.5392   1.237             0.216831    
## concep_2010         -64.7424    77.5397  -0.835             0.404217    
## concep_2011         -40.8999    66.3215  -0.617             0.537773    
## concep_2012         -94.0865    86.3586  -1.089             0.276566    
## concep_2013               NA         NA      NA                   NA    
## maternal_age         58.6162    28.9951   2.022             0.043854 *  
## any_smoker         -137.0995   104.1625  -1.316             0.188824    
## smokeSH             -91.4934    74.1925  -1.233             0.218196    
## mean_cpss             0.1884    28.0725   0.007             0.994649    
## mean_epsd           -14.6595    29.2594  -0.501             0.616620    
## male                119.2181    45.5898   2.615             0.009244 ** 
## mean_o3:mean_temp   -86.1535    24.5931  -3.503             0.000509 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 466.6 on 419 degrees of freedom
## Multiple R-squared:  0.1121, Adjusted R-squared:  0.05917 
## F-statistic: 2.117 on 25 and 419 DF,  p-value: 0.001519
plot(bw_lm)

6 Try a GAM with the ozone and temperature predictor

The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone and temperature to see about potential nonlinear effects

The mean and standard deviation of the mean_o3 variable are 47.81 (2.98) ppb The mean and standard deviation of the mean_temp variable is 52.5 (4.39) degrees F

library(mgcv)
## Loading required package: nlme
## 
## Attaching package: 'nlme'
## The following object is masked from 'package:dplyr':
## 
##     collapse
## This is mgcv 1.8-34. For overview type 'help("mgcv-package")'.
library(tidymv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
#names(gam_df)[2] <- "mean_o3"

head(gam_df)
bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
                lat + lon + lat_lon_int +
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df, method = "REML")
gam.check(bw_gam)

## 
## Method: REML   Optimizer: outer newton
## full convergence after 8 iterations.
## Gradient range [-0.001324346,-0.00126227]
## (score 3211.236 & scale 193952.8).
## Hessian positive definite, eigenvalue range [3.665994,209.8084].
## Model rank =  52 / 53 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                        k'  edf k-index p-value
## s(mean_o3,mean_temp) 29.0 17.9    1.02     0.6
summary(bw_gam)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##                Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)    3365.787     92.388  36.431 < 0.0000000000000002 ***
## lat           -2496.029  23705.662  -0.105              0.91620    
## lon            1221.293  11160.107   0.109              0.91291    
## lat_lon_int   -3027.331  28853.310  -0.105              0.91649    
## ed_no_hs         92.295    135.968   0.679              0.49766    
## ed_hs            18.361    101.005   0.182              0.85584    
## ed_aa            74.299     74.448   0.998              0.31888    
## ed_4yr           44.317     53.212   0.833              0.40543    
## low_bmi        -231.999    124.833  -1.858              0.06383 .  
## ovwt_bmi         -5.915     54.924  -0.108              0.91429    
## obese_bmi        81.417     68.512   1.188              0.23538    
## concep_spring   -35.688     86.213  -0.414              0.67913    
## concep_summer  -175.477    128.764  -1.363              0.17371    
## concep_fall     -46.658    127.841  -0.365              0.71533    
## concep_2010     -82.959     79.747  -1.040              0.29883    
## concep_2011     -65.399     67.113  -0.974              0.33041    
## concep_2012     -87.596     90.803  -0.965              0.33528    
## concep_2013       0.000      0.000      NA                   NA    
## maternal_age     54.777     27.790   1.971              0.04939 *  
## any_smoker     -128.222     99.068  -1.294              0.19631    
## smokeSH        -105.556     71.127  -1.484              0.13858    
## mean_cpss         3.976     27.151   0.146              0.88365    
## mean_epsd       -30.141     28.155  -1.071              0.28501    
## male            120.075     43.590   2.755              0.00614 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                       edf Ref.df     F  p-value    
## s(mean_o3,mean_temp) 17.9  22.98 2.749 0.000035 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Rank: 52/53
## R-sq.(adj) =  0.162   Deviance explained = 23.7%
## -REML = 3211.2  Scale est. = 1.9395e+05  n = 445
save(gam_df, bw_gam, file = here::here("Results", "BW_GAM_v4b.rdata"))
library(mgcViz)
## Loading required package: qgam
## Loading required package: rgl
## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2
## Registered S3 method overwritten by 'mgcViz':
##   method from  
##   +.gg   GGally
## 
## Attaching package: 'mgcViz'
## The following objects are masked from 'package:stats':
## 
##     qqline, qqnorm, qqplot
gam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4b.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)  

7 GAM Sensitivity Analysis

The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.

Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.

library(mgcv)

gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)
##  [1] "birth_weight"  "mean_o3"       "mean_temp"     "lat"          
##  [5] "lon"           "lat_lon_int"   "ed_no_hs"      "ed_hs"        
##  [9] "ed_aa"         "ed_4yr"        "low_bmi"       "ovwt_bmi"     
## [13] "obese_bmi"     "concep_spring" "concep_summer" "concep_fall"  
## [17] "concep_2010"   "concep_2011"   "concep_2012"   "concep_2013"  
## [21] "maternal_age"  "any_smoker"    "smokeSH"       "mean_cpss"    
## [25] "mean_epsd"     "male"
head(gam_df)
gam_df2 <- gam_df %>%
  filter(mean_o3 > -2 & mean_o3 < 2) %>%
  filter(mean_temp > -2 & mean_temp < 2)
hist(gam_df2$mean_o3)

hist(gam_df2$mean_temp)

bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) + 
                lat + lon + lat_lon_int +
                ed_no_hs + ed_hs + ed_aa + ed_4yr + 
                low_bmi + ovwt_bmi + obese_bmi + 
                concep_spring + concep_summer + concep_fall +
                concep_2010 + concep_2011 + concep_2012 + concep_2013 +
                maternal_age + any_smoker + smokeSH + 
                mean_cpss + mean_epsd + male,
              data = gam_df2, method = "REML")
gam.check(bw_gam2)

## 
## Method: REML   Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-0.000632231,0.001433747]
## (score 3103.602 & scale 189210.4).
## Hessian positive definite, eigenvalue range [0.4706214,203.5373].
## Model rank =  52 / 53 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                         k'   edf k-index p-value
## s(mean_o3,mean_temp) 29.00  7.61    0.99    0.42
summary(bw_gam2)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int + 
##     ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi + 
##     obese_bmi + concep_spring + concep_summer + concep_fall + 
##     concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age + 
##     any_smoker + smokeSH + mean_cpss + mean_epsd + male
## 
## Parametric coefficients:
##               Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)    3204.53     104.79  30.581 <0.0000000000000002 ***
## lat           10154.91   23417.30   0.434              0.6648    
## lon           -4744.59   11024.47  -0.430              0.6672    
## lat_lon_int   12366.92   28502.69   0.434              0.6646    
## ed_no_hs         88.57     133.59   0.663              0.5077    
## ed_hs            31.34      99.91   0.314              0.7539    
## ed_aa            96.34      73.94   1.303              0.1934    
## ed_4yr           54.99      52.66   1.044              0.2970    
## low_bmi        -216.33     122.61  -1.764              0.0784 .  
## ovwt_bmi        -29.33      54.34  -0.540              0.5897    
## obese_bmi        72.50      67.66   1.071              0.2846    
## concep_spring    39.66      82.53   0.481              0.6311    
## concep_summer   -19.76     117.26  -0.168              0.8663    
## concep_fall      69.69     113.39   0.615              0.5392    
## concep_2010      48.51      84.78   0.572              0.5676    
## concep_2011      54.23      73.19   0.741              0.4592    
## concep_2012       0.00       0.00      NA                  NA    
## concep_2013     113.81      85.39   1.333              0.1834    
## maternal_age     56.20      27.51   2.043              0.0417 *  
## any_smoker     -134.60      97.46  -1.381              0.1680    
## smokeSH        -121.30      70.20  -1.728              0.0848 .  
## mean_cpss        11.12      26.89   0.413              0.6795    
## mean_epsd       -31.43      27.73  -1.133              0.2577    
## male             93.79      43.30   2.166              0.0309 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                        edf Ref.df     F p-value
## s(mean_o3,mean_temp) 7.611  10.68 0.735   0.723
## 
## Rank: 52/53
## R-sq.(adj) =  0.0544   Deviance explained = 11.9%
## -REML = 3103.6  Scale est. = 1.8921e+05  n = 433
save(gam_df2, bw_gam2, file = here::here("Results", "BW_GAM_Sensitivity_v4b.rdata"))
library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) + 
  l_fitRaster() + l_fitContour() + l_points() +
  labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
  guides(fill=guide_legend(title="Change in\nbirth weight (g)"))

ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4b.jpeg"),
       device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)